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tanglement 



THE GREATEST 



MYSTERY IN 
PHYSICS 



LU 
N 
O 
< 

Q 



FERMAT'S LAST THEOREM THE MYSTERY OF THE ALEPH 



ENTANGLEMENT 



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ENTANGLEMENT 



The Greatest Mystery in Physics 



AMIR D. ACZEL 



FOUR WALLS EIGHT WINDOWS 
NEW YORK 



© 2001 Amir D. Aczel 

Published in the United States by: 
Four Walls Eight Windows 
39 West 14th Street, room 503 
New York, N.Y., 10011 

Visit our website at http://www.4w8w.com 

First printing September 2002. 

All rights reserved. No part of this book may be reproduced, stored in 
a data base or other retrieval system, or transmitted in any form, by 
any means, including mechanical, electronic, photocopying, recording, 
or otherwise, without the prior written permission of the publisher. 

Library of Congress Cataloging-in-Publication Data: 

Entanglement: the greatest mystery in physics/ by Amir D. Aczel. 

p. cm. 
Includes bibliographical references and index. 

isbn 1-56858-232-3 

1. Quantum theory. I. Title. 
QC174.12.A29 2002 
530.12 — dc2i 2002069338 

10 987654321 

Printed in the United States 

Typeset and designed by Terry Bain 

Illustrations, unless otherwise noted, by Ortelius Design. 



for liana 



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Contents 

Preface / ix 

A Mysterious Force of Harmony / 1 

Before the Beginning / 7 

Thomas Young's Experiment / 17 

Planck's Constant / 29 

The Copenhagen School / 37 

De Broglie's Pilot Waves / 49 

Schrodinger and His Equation / 55 

Heisenberg's Microscope / 73 

Wheeler's Cat/ 83 

The Hungarian Mathematician / 95 

Enter Einstein / 103 

Bohm and Aharanov / 123 

John Bell's Theorem / 137 

The Dream of Clauser, Home, and Shimony / 149 

Alain Aspect / 177 

Laser Guns / 191 

Triple Entanglement / 203 

The Ten-Kilometer Experiment / 235 

Teleportation: "Beam Me Up, Scotty" / 241 

Quantum Magic: What Does It All Mean? / 249 

Acknowledgements / 255 

References / 266 

Index / 269 



Vll 



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Preface 



"My own suspicion is that the universe is not only queerer 
than we suppose, but queerer than we can suppose." 

— J.B.S. Haldane 



Jn the fall of 1972, I was an undergraduate in mathe- 
matics and physics at the University of California at 
Berkeley. There I had the good fortune to attend a spe- 
cial lecture given on campus by Werner Heisenberg, one of 
the founders of the quantum theory. While today I have some 
reservations about the role Heisenberg played in history — at 
the time other scientists left in protest of Nazi policies, he 
stayed behind and was instrumental in Hitler's attempts to 
develop the Bomb — nevertheless his talk had a profound, 
positive effect on my life, for it gave me a deep appreciation 
for the quantum theory and its place in our efforts to under- 
stand nature. 

Quantum mechanics is the strangest field in all of science. 
From our everyday perspective of life on Earth, nothing 



IX 



ENTANGLEMENT 



makes sense in quantum theory, the theory about the laws of 
nature that govern the realm of the very small (as well as 
some large systems, such as superconductors). The word 
itself, quantum, denotes a small packet of energy — a very 
small one. In quantum mechanics, as the quantum theory is 
called, we deal with the basic building blocks of matter, the 
constituent particles from which everything in the universe is 
made. These particles include atoms, molecules, neutrons, 
protons, electrons, quarks, as well as photons — the basic 
units of light. All these objects (if indeed they can be called 
objects) are much smaller than anything the human eye can 
see. At this level, suddenly, all the rules of behavior with 
which we are familiar no longer hold. Entering this strange 
new world of the very small is an experience as baffling and 
bizarre as Alice's adventures in Wonderland. In this unreal 
quantum world, particles are waves, and waves are particles. 
A ray of light, therefore, is both an electromagnetic wave 
undulating through space, and a stream of tiny particles 
speeding toward the observer, in the sense that some quan- 
tum experiments or phenomena reveal the wave nature of 
light, while others the particle nature of the same light — but 
never both aspects at the same time. And yet, before we 
observe a ray of light, it is both a wave and a stream of 
particles. 

In the quantum realm everything is fuzzy — there is a hazy 
quality to all the entities we deal with, be they light or elec- 
trons or atoms or quarks. An uncertainty principle reigns in 
quantum mechanics, where most things cannot be seen or 
felt or known with precision, but only through a haze of 
probability and chance. Scientific predictions about outcomes 



PREFACE C® XI 



are statistical in nature and are given in terms of probabili- 
ties — we can only predict the most likely location of a parti- 
cle, not its exact position. And we can never determine both 
a particle's location and its momentum with good accuracy. 
Furthermore, this fog that permeates the quantum world can 
never go away. There are no "hidden variables," which, if 
known, would increase our precision beyond the natural 
limit that rules the quantum world. The uncertainty, the 
fuzziness, the probabilities, the dispersion simply cannot go 
away — these mysterious, ambiguous, veiled elements are an 
integral part of this wonderland. 

Even more inexplicable is the mysterious superposition of 
states of quantum systems. An electron (a negatively-charged 
elementary particle) or photon (a quantum of light) can be in 
a superposition of two or more states. No longer do we speak 
about "here or there;" in the quantum world we speak about 
"here and there." In a certain sense, a photon, part of a 
stream of light shone on a screen with two holes, can go 
through both holes at the same time, rather than the expected 
choice of one hole or the other. The electron in orbit around 
the nucleus is potentially at many locations at the same time. 

But the most perplexing phenomenon in the bizarre world 
of the quantum is the effect called entanglement. Two parti- 
cles that may be very far apart, even millions or billions of 
miles, are mysteriously linked together. Whatever happens 
to one of them immediately causes a change in the other one. 1 

What I learned from Heisenberg's lecture thirty years ago 
was that we must let go of all our preconceptions about the 
world derived from our experience and our senses, and 
instead let mathematics lead the way. The electron lives in a 



Xll & ENTANGLEMENT 



different space from the one in which we live. It lives in what 
mathematicians call a Hilbert space, and so do the other tiny 
particles and photons. This Hilbert space, developed by 
mathematicians independently of physics, seems to describe 
well the mysterious rules of the quantum world — rules that 
make no sense when viewed with an eye trained by our every- 
day experiences. So the physicist working with quantum sys- 
tems relies on the mathematics to produce predictions of the 
outcomes of experiments or phenomena, since this same 
physicist has no natural intuition about what goes on inside 
an atom or a ray of light or a stream of particles. Quantum 
theory taxes our very concept of what constitutes science — 
for we can never truly "understand" the bizarre behavior of 
the very small. And it taxes our very idea of what constitutes 
reality. What does "reality" mean in the context of the exis- 
tence of entangled entities that act in concert even while vast 
distances apart? 

The beautiful mathematical theory of Hilbert space, 
abstract algebra, and probability theory — our mathematical 
tools for handling quantum phenomena — allow us to pre- 
dict the results of experiments to a stunning level of accu- 
racy; but they do not bring us an understanding of the 
underlying processes. Understanding what really happens 
inside the mysterious box constituting a quantum system 
may be beyond the powers of human beings. According to 
one interpretation of quantum mechanics, we can only use 
the box to predict outcomes. And these predictions are sta- 
tistical in nature. 

There is a very strong temptation to say: "Well, if the 



PREFACE & Xlll 



theory cannot help us understand what truly goes on, then 
the theory is simply not complete. Something is missing — 
there must be some missing variables, which, once added to 
our equations, would complete our knowledge and bring us 
the understanding we seek." And, in fact, the greatest scien- 
tist of the twentieth century, Albert Einstein, posed this very 
challenge to the nascent quantum theory. Einstein, whose 
theories of relativity revolutionized the way we view space 
and time, argued that quantum mechanics was excellent as a 
statistical theory, but did not constitute a complete descrip- 
tion of physical reality. His well-known statement that "God 
doesn't play dice with the world" was a reflection of his belief 
that there was a deeper, non-probabilistic layer to the quan- 
tum theory which had yet to be discovered. Together with 
his colleagues Podolsky and Rosen, he issued a challenge to 
quantum physics in 1935, claiming that the theory, was 
incomplete. The three scientists based their argument on the 
existence of the entanglement phenomenon, which in turn 
had been deduced to exist based on mathematical consider- 
ations of quantum systems. 

At his talk at Berkeley in 1972, Heisenberg told the story 
of his development of the approach to the quantum theory 
called matrix mechanics. This was one of his two major con- 
tributions to the quantum theory, the other being the uncer- 
tainty principle. Heisenberg recounted how, when aiming to 
develop his matrix approach in 1925, he did not even know 
how to multiply matrices (an elementary operation in math- 
ematics). But he taught himself how to do so, and his theory 
followed. Mathematics thus gave scientists the rules of 



XIV & ENTANGLEMENT 

behavior in the quantum world. Mathematics also led 
Schrodinger to his alternative, and simpler, approach to 
quantum mechanics, the wave equation. 

Over the years, I've followed closely the developments in 
the quantum theory. My books have dealt with mysteries in 
mathematics and physics. Fermafs Last Theorem told the 
story of the amazing proof of a problem posed long ago; 
God's Equation was the tale of Einstein's cosmological con- 
stant and the expansion of the universe; The Mystery of the 
Aleph was a description of humanity's attempt to understand 
infinity. But I've always wanted to address the secrets of the 
quantum. A recent article in The New York Times provided 
me with the impetus I needed. The article dealt with the chal- 
lenge Albert Einstein and his two colleagues issued to the 
quantum theory, claiming that a theory that allowed for the 
"unreal" phenomenon of entanglement had to be incomplete. 

Seven decades ago, Einstein and his scientific allies imagined 
ways to prove that quantum mechanics, the strange rules that 
describe the world of the very small, were just too spooky to 
be true. Among other things, Einstein showed that, according 
to quantum mechanics, measuring one particle could instantly 
change the properties of another particle, no matter how far 
apart they were. He considered this apparent action-at-a-dis- 
tance, called entanglement, too absurd to be found in nature, 
and he wielded his thought experiments like a weapon to 
expose the strange implications that this process would have 
if it could happen. But experiments described in three forth- 
coming papers in the journal Physical Review Letters give a 
measure of just how badly Einstein has been routed. The 



PREFACE & XV 

experiments show not only that entanglement does happen — 
which has been known for some time — but that it might be 
used to create unbreakable codes . . . 2 

As I knew from my study of the life and work of Albert Ein- 
stein, even when Einstein thought he was wrong (about the 
cosmological constant), he was right. And as for the quantum 
world — Einstein was one of the developers of the theory. I 
knew quite well that — far from being wrong — Einstein's 
paper of 193 5, obliquely alluded to in the Times article, was 
actually the seed for one of the most important discoveries in 
physics in the twentieth century: the actual discovery of 
entanglement through physical experiments. This book tells 
the story of the human quest for entanglement, the most 
bizarre of all the strange aspects of quantum theory. 

Entangled entities (particles or photons) are linked together 
because they were produced by some process that bound 
them together in a special way. For example, two photons 
emitted from the same atom as one of its electrons descends 
down two energy levels are entangled. (Energy levels are 
associated with the orbit of an electron in the atom.) While 
neither flies off in a definite direction, the pair will always be 
found on opposite sides of the atom. And such photons or 
particles, produced in a way that links them together, remain 
intertwined forever. Once one is changed, its twin — wher- 
ever it may be in the universe — will change instantaneously. 

In 1935, Einstein, together with his colleagues Rosen and 
Podolsky, considered a system of two distinct particles that 
was permissible under the rules of quantum mechanics. The 
state of this system was shown to be entangled. Einstein, 



XVI & ENTANGLEMENT 



Podolsky, and Rosen used this theoretical entanglement of 
separated particles to imply that if quantum mechanics 
allowed such bizarre effects to exist, then something must be 
wrong, or incomplete, as they put it, about the theory. 

In 1957, the physicists David Bohm and Yakir Aharonov 
analyzed the results of an experiment that had been per- 
formed by C.S. Wu and I. Shaknov almost a decade earlier, 
and their analysis provided the first hint that entanglement of 
separated systems may indeed take place in nature. Then in 
1972, two American physicists, John Clauser and Stuart 
Freedman, produced evidence that entanglement actually 
exists. And a few years later, the French physicist Alain 
Aspect and his colleagues provided more convincing and 
complete evidence for the existence of the phenomenon. Both 
groups followed the seminal theoretical work in this area by 
John S. Bell, an Irish physicist working in Geneva, and set out 
to prove that the Einstein-Podolsky-Rosen thought experi- 
ment was not an absurd idea to be used to invalidate the 
completeness of the quantum theory, but rather the descrip- 
tion of a real phenomenon. The existence of the phenomenon 
provides evidence in favor of quantum mechanics and against 
a limiting view of reality. 



A NOTE TO THE READER 

Quantum theory itself, and in particular the concept of 
entanglement, is very difficult for anyone to understand — 
even for accomplished physicists or mathematicians. I there- 
fore structured the book in such a way that the ideas and 



PREFACE & XVII 



concepts discussed are constantly being explained and re- 
explained in various forms. This approach makes sense when 
one considers the fact that some of the brightest scientists 
today have spent lifetimes working on entanglement; the 
truth is that even after decades of research, it is difficult to 
find someone who will admit to understanding the quantum 
theory perfectly well. These physicists know how to apply 
the rules of quantum mechanics in a variety of situations. 
They can perform calculations and make predictions to a 
very high degree of accuracy, which is rare in some other 
areas. But often these bright scientists will profess that they 
do not truly understand what goes on in the quantum world. 
It is exactly for this reason that in chapter after chapter in this 
book I repeat the concepts of quantum theory and entangle- 
ment, every time from a slightly different angle, or as 
explained by a different scientist. 

I have made an effort to incorporate the largest possible 
number of original figures, obtained from scientists, describing 
actual experiments and designs. My hope is that these figures 
and graphs will help the reader understand the mysterious and 
wonderful world of the quantum and the setting within which 
entanglement is produced and studied. In addition, where 
appropriate, I have incorporated a number of equations and 
symbols. I did so not to baffle the reader, but so that readers 
with an advanced preparation in science might gain more from 
the presentation. For example, in the chapter on Schrodinger's 
work I include the simplest (and most restricted) form of 
Schrodinger's famous equation for the benefit of those who 
might want to see what the equation looks like. It is perfectly 
fine for a reader, if she so chooses, to skip over the equations 



XVlll & ENTANGLEMENT 

and read on, and anyone doing so will suffer no loss of infor- 
mation or continuity. 

This is a book about science, the making of science, the 
philosophy that underlies science, the mathematical under- 
pinnings of science, the experiments that verify and expose 
nature's inner secrets, and the lives of the scientists who pur- 
sue nature's most bizarre effect. These scientists constitute a 
group of the greatest minds of the twentieth century, and 
their combined lifetimes span the entire century. These 
people, relentlessly in search of knowledge about a deep mys- 
tery of nature — entanglement — led and lead lives today that 
are, themselves, entangled with one another. This book tells 
the story of this search, one of the greatest scientific detective 
stories in history. And while the science of entanglement has 
also brought about the birth of new and very exciting tech- 
nologies, the focus of this book is not on the technologies 
spawned by the research. Entanglement is about the search 
called modern science. 



A Mysterious Force of Harmony 



"Alas, to wear the mantle of Galileo it is not enough that 
you be persecuted by an unkind establishment, you must 
also be right." 

—Robert Park 



Js it possible that something that happens here will 
instantaneously make something happen at a far away 
location? If we measure something in a lab, is it possi- 
ble that at the same moment, a similar event takes place ten 
miles away, on the other side of the world, or on the other 
side of the universe? Surprisingly, and against every intuition 
we may possess about the workings of the universe, the 
answer is yes. This book tells the story of entanglement, a 
phenomenon in which two entities are inexorably linked no 
matter how far away from each other they may be. It is the 
story of the people who have spent lifetimes seeking evidence 
that such a bizarre effect — predicted by the quantum theory 
and brought to wide scientific attention by Einstein — is 
indeed an integral part of nature. 

As these scientists studied such effects, and produced defin- 



ENTANGLEMENT 



itive evidence that entanglement is a reality, they have also 
discovered other, equally perplexing, aspects of the phenom- 
enon. Imagine Alice and Bob, two happily married people. 
While Alice is away on a business trip, Bob meets Carol, who 
is married to Dave. Dave is also away at that time, on the 
other side of the world and nowhere near any of the other 
three. Bob and Carol become entangled with each other; they 
forget their respective spouses and now strongly feel that they 
are meant to stay a couple forever. Mysteriously, Alice and 
Dave — who have never met — are now also entangled with 
each other. They suddenly share things that married people 
do, without ever having met. If you substitute for the people 
in this story particles labeled A, B, C, and D, then the bizarre 
outcome above actually occurs. If particles A and B are 
entangled, and so are C with D, then we can entangle the 
separated particles A and D by passing B and C through an 
apparatus that entangles them together. 

Using entanglement, the state of a particle can also be tele- 
ported to a faraway destination, as happens to Captain Kirk 
on the television series "Star Trek" when he asks to be 
beamed back up to the Enterprise. To be sure, no one has 
yet been able to teleport a person. But the state of a quantum 
system has been teleported in the laboratory. Furthermore, 
such incredible phenomena can now be used in cryptography 
and computing. 

In such futuristic applications of technology, the entangle- 
ment is often extended to more than two particles. It is pos- 
sible to create triples of particles, for example, such that all 
three are 100% correlated with each other — whatever hap- 
pens to one particle causes a similar instantaneous change in 



A MYSTERIOUS FORCE OF HARMONY © 3 

the other two. The three entities are thus inexorably inter- 
linked, wherever they may be. 

One day in 1968, physicist Abner Shimony was sitting in his 
office at Boston University. His attention was pulled, as if by 
a mysterious force, to a paper that had appeared two years 
earlier in a little-known physics journal. Its author was John 
Bell, an Irish physicist working in Geneva. Shimony was one 
of very few people who had both the ability and the desire to 
truly understand Bell's ideas. He knew that Bell's theorem, as 
explained and proved in the paper, allowed for the possibil- 
ity of testing whether two particles, located far apart from 
each other, could act in concert. Shimony had just been asked 
by a fellow professor at Boston University, Charles Willis, if 
he would be willing to direct a new doctoral student, Michael 
Home, in a thesis on statistical mechanics. Shimony agreed 
to see the student, but was not eager to take on a Ph.D. stu- 
dent in his first year of teaching at Boston University. In any 
case, he said, he had no good problem to suggest in statisti- 
cal mechanics. But, thinking that Home might find a prob- 
lem in the foundations of quantum mechanics interesting, he 
handed him Bell's paper. As Shimony put it, "Home was 
bright enough to see quickly that Bell's problem was inter- 
esting." Michael Home took Bell's paper home to study, and 
began work on the design of an experiment that would use 
Bell's theorem. 

Unbeknownst to the two physicists in Boston, at Columbia 
University in New York, John F. Clauser was reading the 
same paper by Bell. He, too, was mysteriously drawn to the 



ENTANGLEMENT 



problem suggested by Bell, and recognized the opportunity 
for an actual experiment. Clauser had read the paper by Ein- 
stein, Podolsky, and Rosen, and thought that their sugges- 
tion was very plausible. Bell's theorem showed a discrepancy 
between quantum mechanics and the "local hidden vari- 
ables" interpretation of quantum mechanics offered by Ein- 
stein and his colleagues as an alternative to the "incomplete" 
quantum theory, and Clauser was excited about the possi- 
bility of an experiment exploiting this discrepancy. Clauser 
was skeptical, but he couldn't resist testing Bell's predictions. 
He was a graduate student, and everyone he talked to told 
him to leave it alone, to get his Ph.D., and not to dabble in 
science fiction. But Clauser knew better. The key to quantum 
mechanics was hidden within Bell's paper, and Clauser was 
determined to find it. 

Across the Atlantic, a few years later, Alain Aspect was fever- 
ishly working in his lab in the basement of the Center for 
Research on Optics of the University of Paris in Orsay. He 
was racing to construct an ingenious experiment: one that 
would prove that two photons, at two opposite sides of his 
lab, could instantaneously affect each other. Aspect was led 
to his ideas by the same abstruse paper by John Bell. 

In Geneva, Nicholas Gisin met John Bell, read his papers and 
was also thinking about Bell's ideas. He, too, was in the race 
to find an answer to the same crucial question: a question 
that had deep implications about the very nature of reality. 
But we are getting ahead of ourselves. The story of Bell's 
ideas, which goes back to a suggestion made thirty-five years 



A MYSTERIOUS FORCE OF HARMONY 



earlier by Albert Einstein, has its origins in humanity's quest 
for knowledge of the physical world. And in order to truly 
understand these deep ideas, we must return to the past. 



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Before the Beginning 



"Out yonder there was this huge world, which exists inde- 
pendently of us human beings and which stands before us 
like a great, eternal riddle, at least partially accessible to 
our inspection." 

— Albert Einstein 

"The mathematics of quantum mechanics is straightfor- 
ward, but making the connection between the mathematics 
and an intuitive picture of the physical world is very hard" 

— Claude N. Cohen-Tannoudji 



Jn the book of Genesis we read: "God said: Let there be 
light." God then created heaven and earth and all things 
that filled them. Humanity's quest for an understanding 
of light and matter goes back to the dawn of civilization; 
they are the most basic elements of the human experience. 
And, as Einstein showed us, the two are one and the same: 
both light and matter are forms of energy. People have always 
striven to understand what these forms of energy mean. 
What is the nature of matter? And what is light? 

The ancient Egyptians and Babylonians and their succes- 
sors the Phoenicians and the Greeks tried to understand the 
mysteries of matter, and of light and sight and color. The 
Greeks looked at the world with the first modern intellectual 
eyes. With their curiosity about numbers and geometry, cou- 



ENTANGLEMENT 



pled with a deep desire to understand the inner workings of 
nature and their environment, they gave the world its first 
ideas about physics and logic. 

To Aristotle (300 B.C.), the sun was a perfect circle in the 
sky, with no blemishes or imperfections. Eratosthenes of 
Cyrene (c. 276 B.C. -194 B.C.) estimated the circumference of 
our planet by measuring the angle sunlight was making at 
Syene (modern Aswan), in Upper Egypt, against the angle it 
made at the same time farther north, in Alexandria. He came 
stunningly close to the earth's actual circumference of 25,000 
miles. 

The Greek philosophers Aristotle and Pythagoras wrote 
about light and its perceived properties; they were fascinated 
by the phenomenon. But the Phoenicians were the first people 
in history to make glass lenses, which allowed them to mag- 
nify objects and to focus light rays. Archaeologists have 
found 3,000-year-old magnifying glasses in the region of the 
eastern Mediterranean that was once Phoenicia. Interestingly, 
the principle that makes a lens work is the slowing-down of 
light as it travels through glass. 

The Romans learned glass-making from the Phoenicians, 
and their own glassworks became one of the important 
industries of the ancient world. Roman glass was of high 
quality and was even used for making prisms. Seneca (5 B.C.- 
A.D. 45) was the first to describe a prism and the breaking- 
down of white light into its component colors. This 
phenomenon, too, is based on the speed of light. We have no 
evidence of any experiments carried out in antiquity to deter- 
mine the speed of light. It seems that ancient peoples thought 
that light moved instantly from place to place. Because light 



BEFORE THE BEGINNING 



is so fast, they could not detect the infinitesimal delays as 
light traveled from source to destination. The first attempt to 
study the speed of light did not come for another 1,600 years. 

Galileo was the first person known to have attempted to 
estimate the speed of light. Once again, experimentation with 
light had a close connection with glassmaking. After the 
Roman Empire collapsed in the fifth century, many Romans 
of patrician and professional backgrounds escaped to the 
Venetian lagoons and established the republic of Venice. 
They brought with them the art of making glass, and thus the 
glassworks on the island of Murano were established. 
Galileo's telescopes were of such high quality — in fact they 
were far better than the first telescopes made in Holland — 
because he used lenses made of Murano glass. It was with the 
help of these telescopes that he discovered the moons of 
Jupiter and the rings of Saturn and determined that the Milky 
Way is a large collection of stars. 

In 1607, Galileo conducted an experiment on two hilltops 
in Italy, in which a lantern on one hill was uncovered. When 
an assistant on the other hilltop saw the light, he opened his 
own lantern. The person on the first hill tried to estimate 
the time between opening the first lantern and seeing the 
light return from the second one. Galileo's quaint experi- 
ment failed, however, because of the tiny length of time 
elapsed between the sending of the first lantern signal and 
the return of the light from the other hilltop. It should be 
noted, anyway, that much of this time interval was due to 
the human response time in uncovering the second lantern 
rather than to the actual time light took to travel this 
distance. 



10 & ENTANGLEMENT 



Almost seventy years later, in 1676, the Danish astronomer 
Olaf Romer became the first scientist to calculate the speed 
of light. He accomplished this task by using astronomical 
observations of the moons of Jupiter, discovered by Galileo. 
Romer devised an intricate and extremely clever scheme by 
which he recorded the times of the eclipses of the moons of 
Jupiter. He knew that the earth orbits the sun, and that there- 
fore the earth would be at different locations in space vis-a- 
vis Jupiter and its moons. Romer noticed that the times of 
disappearance of the moons of Jupiter behind the planet were 
not evenly spaced. As Earth and Jupiter orbit the sun, their 
distance from each other varies. Thus the light that brings 
us information on an eclipse of a Jovian moon takes differ- 
ent lengths of time to arrive on Earth. From these differences, 
and using his understanding of the orbits of Earth and 
Jupiter, Romer was able to calculate the speed of light. His 
estimate, 140,000 miles per second, was not quite the actual 
value of 186,000 miles per second. However, considering the 
date of the discovery and the fact that time was not measur- 
able to great accuracy using the clocks of the seventeenth 
century, his achievement — the first measurement of the speed 
of light and the first proof that light does not travel at infi- 
nite speed — is an immensely valuable landmark in the his- 
tory of science. 

Descartes wrote about optics in 1638 in his book 
Dioptrics, stating laws of the propagation of light: the laws 
of reflection and refraction. His work contained the seed of 
the most controversial idea in the field of physics: the ether. 
Descartes put forward the hypothesis that light propagates 
through a medium, and he named this medium the ether. Sci- 



BEFORE THE BEGINNING & II 

ence would not be rid of the ether for another three hundred 
years, until Einstein's theory of relativity would finally deal 
the ether its fatal blow. 

Christiaan Huygens (1629-1695) and Robert Hooke 
(1635-1703) proposed the theory that light is a wave. Huy- 
gens, who as a sixteen-year-old boy had been tutored by 
Descartes during his stay in Holland, became one of the 
greatest thinkers of the day. He developed the first pendu- 
lum clock and did other work in mechanics. His most 
remarkable achievement, however, was a theory about the 
nature of light. Huygens interpreted Romer's discovery of 
the finite speed of light as implying that light must be a wave 
propagating through some medium. On this hypothesis, 
Huygens constructed an entire theory. Huygens visualized 
the medium as the ether, composed of an immense number of 
tiny, elastic particles. When these particles were excited into 
vibration, they produced light waves. 

In 1692, Isaac Newton (1643-1727) finished his book 
Opticks about the nature and propagation of light. The book 
was lost in a fire in his house, so Newton rewrote it for pub- 
lication in 1704. His book issued a scathing attack on Huy- 
gens's theory, and argued that light was not a wave but 
instead was composed of tiny particles traveling at speeds 
that depend on the color of the light. According to Newton, 
there are seven colors in the rainbow: red, yellow, green, blue, 
violet, orange, and indigo. Each color has its own speed of 
propagation. Newton derived his seven colors by an analogy 
with the seven main intervals of the musical octave. Further 
editions of his book continued Newton's attacks on Huy- 
gens's theories and intensified the debate as to whether light 



12 & ENTANGLEMENT 



is a particle or a wave. Surprisingly, Newton — who co-dis- 
covered the calculus and was one of the greatest mathemati- 
cians of all time — never bothered to address Romer's findings 
about the speed of light, and neither did he give the wave 
theory the attention it deserved. 

But Newton, building on the foundation laid by Descartes, 
Galileo, Kepler, and Copernicus, gave the world classical 
mechanics, and, through it, the concept of causality. New- 
ton's second law says that force is equal to mass times accel- 
eration: F=ma. Acceleration is the second derivative of 
position (it is the rate of change of the speed; and speed, in 
turn, is the rate of change of position). Newton's law is there- 
fore an equation with a (second) derivative in it. It is called 
a (second-order) differential equation. Differential equations 
are very important in physics, since they model change. New- 
ton's laws of motion are a statement about causality. They 
deal with cause and effect. If we know the initial position 
and velocity of a massive body, and we know the force act- 
ing on it and the force's direction, then we should be able to 
determine a final outcome: where will the body be at a later 
point in time. 

Newton's beautiful theory of mechanics can predict the 
motion of falling bodies as well as the orbits of planets. We 
can use these cause-and-effect relationships to predict where 
an object will go. Newton's theory is a tremendous edifice 
that explains how large bodies — things we know from every- 
day life — can move from place to place, as long as their speeds 
or masses are not too great. For velocities approaching the 
speed of light, or masses of the order of magnitude of stars, 
Einstein's general relativity is the correct theory, and classical, 



BEFORE THE BEGINNING & 13 

Newtonian mechanics breaks down. It should be noted, how- 
ever, that Einstein's theories of special and general relativity 
hold, with improvements over Newton, even in situations in 
which Newtonian mechanics is a good approximation. 

Similarly, for objects that are very small — electrons, atoms, 
photons — Newton's theory breaks down as well. With it, we 
also lose the concept of causality. The quantum universe does 
not possess the cause-and-effect structure we know from 
everyday life. Incidentally, for small particles moving at 
speeds close to that of light, relativistic quantum mechanics 
is the right theory. 

One of the most important principles in classical physics — 
and one that has great relevance to our story — is the princi- 
ple of conservation of momentum. Conservation principles 
for physical quantities have been known to physicists for over 
three centuries. In his book, the Principia, of 1687, Newton 
presented his laws for the conservation of mass and momen- 
tum. In 1840, the German physician Julius Robert Mayer 
(1812-1878) deduced that energy was conserved as well. 
Mayer was working as a ship's surgeon on a voyage from 
Germany to Java. While treating members of the ship's crew 
for various injuries in the tropics, Dr. Mayer noticed that the 
blood oozing from their wounds was redder than the blood 
he saw in Germany. Mayer had heard of Lavoisier's theory 
that body heat came from the oxidation of sugar in body tis- 
sue using oxygen from the blood. He reasoned that in the 
warm tropics the human body needed to produce less heat 
than it would in colder northern Europe, and hence that 
more oxygen remained in the blood of people in the tropics, 
making the blood redder. Using arguments about how the 



14 C® ENTANGLEMENT 

body interacts with the environment — giving and receiving 
heat — Mayer postulated that energy was conserved. This idea 
was derived experimentally by Joule, Kelvin, and Carnot. 
Earlier, Leibniz had discovered that kinetic energy can be 
transformed into potential energy and vice versa. 

Energy in any of its forms (including mass) is conserved — 
that is, it cannot be created out of nothing. The same holds 
true for momentum, angular momentum, and electric charge. 
The conservation of momentum is very important to our 
story. 

Suppose that a moving billiards ball hits a stationary one. 
The moving ball has a particular momentum associated with 
it — the product of its mass by its speed, p-mv. This product 
of mass times speed, the momentum of the billiards ball, 
must be conserved within the system. Once one ball hits 
another, its speed slows down, but the ball that was hit now 
moves as well. The speed times mass for the system of these 
two objects must be the same as that of the system before 
the collision (the stationary ball had momentum zero, so it's 
the momentum of the moving one that now gets split in two). 
This is demonstrated by the figure below, where after the col- 
lision the two balls travel in different directions. 



BEFORE THE BEGINNING C© I J 




'♦A 




X 



In any physical process, total input momentum equals total 
output momentum. This principle, when applied within the 
world of the very small, will have consequences beyond this 
simple and intuitive idea of conservation. In quantum 
mechanics, two particles that interact with each other at 
some point — in a sense like the two billiards balls of this 
example — will remain intertwined with each other, but to a 
greater extent than billiards balls: whatever should happen to 
one of them, no matter how far it may be from its twin, will 
immediately affect the twin particle. 



This Page Intentionally Left Blank 



Thomas Young's Experiment 



"We choose to examine a phenomenon (the double-slit 
experiment) that is impossible, absolutely impossible, to 
explain in any classical way, and which has in it the heart 
of quantum mechanics. In reality, it contains the only 
mystery. " 

— Richard Feynman 



Thomas Young (1773-1829) was a British physician 
and physicist whose experiment changed the way 
we think about light. Young was a child prodigy 
who learned to read at age two, and by age six had read the 
Bible twice and learned Latin. Before the age of 19, he was 
fluent in thirteen languages, including Greek, French, Ital- 
ian, Hebrew, Chaldean, Syriac, Samaritan, Persian, Ethiopic, 
Arabic, and Turkish. He studied Newton's calculus and his 
works on mechanics and optics, as well as Lavoisier's Ele- 
ments of Chemistry. He also read plays, studied law, and 
learned politics. 

In the late 1700s Young studied medicine in London, Edin- 
burgh, and Gottingen, where he received his M.D. In 1794, 
he was elected to the Royal Society. Three years later, he 
moved to Cambridge University, where he received a second 



17 



ENTANGLEMENT 



M.D. and joined the Royal College of Physicians. After a 
wealthy uncle left him a house in London and a large cash 
inheritance, Young moved to the capital and established a 
medical practice there. He was not a successful doctor, but 
instead devoted his energies to study and scientific experi- 
ments. Young studied vision and gave us the theory that the 
eye contains three types of receptors for light of the three 
basic colors, red, blue, and green. Young contributed to nat- 
ural philosophy, physiological optics, and was one of the first 
to translate Egyptian hieroglyphics. His greatest contribu- 
tion to physics was his effort to win acceptance of the wave 
theory of light. Young conducted the now-famous double- 
slit experiment on light, demonstrating the wave-theory effect 
of interference. 

In his experiment, Young had a light source and a barrier. 
He cut two slits in the barrier, through which the light from 
the source could pass. Then he placed a screen behind the 
barrier. When Young shone the light from the source on the 
barrier with the two slits, he obtained an interference pattern. 

x 

m 



Source 



Wall 



i 

Backstop 




THOMAS YOUNG'S EXPERIMENT C® I<) 



An interference pattern is the hallmark of waves. Waves 
interfere with each other, while particles do not. Richard Feyn- 
man considered Young's result of the double-slit experiment — 
as it appears in the case of electrons and other quanta that can 
be localized — so important that he devoted much of the first 
chapter of the third volume of his renowned textbook, The 
Teynman Lectures on Physics, to this type of experiment. 3 He 
believed that the result of the double-slit experiment was the 
fundamental mystery of quantum mechanics. Richard Feyn- 
man demonstrated in his Lectures the idea of interference of 
waves versus the non-interference of particles using bullets. 
Suppose a gun shoots bullets randomly at a barrier with two 
slits. The pattern is as shown below. 



Gun 



m 



Moveable 
Detector 




m 

Backstop 



Water waves, if passed through a barrier with two slits, 
make the pattern below. Here we find interference, as in the 
Young experiment with light, because we have classical 
waves. The amplitudes of two waves may add to each other, 
producing a peak on the screen, or they may interfere 
destructively, producing a trough. 



20 & ENTANGLEMENT 





So the Young experiment demonstrates that light is a wave. 
But is light really a wave? 

The duality between light as wave and light as a stream of 
particles still remains an important facet of physics in the 
twenty-first century. Quantum mechanics, developed in the 
1920s and 1930s, in fact reinforces the view that light is both 
particle and wave. The French physicist Louis de Broglie 
argued in 1924 that even physical bodies such as electrons 
and other particles possess wave properties. Experiments 
proved him right. Albert Einstein, in deriving the photoelec- 
tric effect in 1905, put forward the theory that light was 
made of particles, just as Newton had argued. Einstein's light 
particle eventually became known as a photon, a name 
derived from the Greek word for light. According to the 
quantum theory, light may be both a wave and a particle, 
and this duality — and apparent paradox — is a mainstay of 
modern physics. Mysteriously, light exhibits both phenomena 
that are characteristic of waves, interference and diffraction, 
and phenomena of particles, localized in their interaction 



THOMAS YOUNG'S EXPERIMENT & 21 

with matter. Two light rays interfere with each other in a way 
that is very similar to sound waves emanating from two 
stereo speakers, for example. On the other hand, light inter- 
acts with matter in a way that only particles can, as happens 
in the photoelectric effect. 

Young's experiment showed that light was a wave. But we 
also know that light is, in a way, a particle: a photon. In the 
twentieth century, the Young experiment was repeated with 
very weak light — light that was produced as one photon at a 
time. Thus, it was very unlikely that several photons would 
be found within the experimental apparatus at the same time. 
Stunningly, the same interference pattern appeared as enough 
time elapsed so that the photons, arriving one at a time, accu- 
mulated on the screen. What was each photon interfering 
with, if it was alone in the experimental apparatus? The 
answer seemed to be: with itself. In a sense, each photon went 
through both slits, not one slit, and as it appeared on the 
other side, it interfered with itself. 

The Young experiment has been carried out with many 
entities we consider to be particles: electrons, since the 1950s; 
neutrons, since the 1970s; and atoms, since the 1980s. In 
each case, the same interference pattern occurred. These find- 
ings demonstrated the de Broglie principle, according to 
which particles also exhibit wave phenomena. For example, 
in 1989, A. Tonomura and colleagues performed a double- 
slit experiment with electrons. Their results are shown below, 
clearly demonstrating an interference pattern. 



XX 



ENTANGLEMENT 




Anton Zeilinger and colleagues demonstrated the same 
pattern for neutrons, traveling at only 2 km/second, in 1991. 
Their results are shown below. 



THOMAS YOUNG'S EXPERIMENT C® Z?, 



4000 



3000 



6 
CO 



1000 




SCANNING SLIT POSITION 



The same pattern was shown with atoms. This demon- 
strated that the duality between particles and waves mani- 
fests itself even for larger entities. 

300 



CO 




SCANNING GRATING POSITION 

Anton Zeilinger and his colleagues at the University of 
Vienna, where Schrodinger and Mach had worked, went one 



M 



ENTANGLEMENT 



step further. They extended our knowledge about quantum 
systems to entities that one would not necessarily associate 
any more with the world of the very small. (Although it 
should be pointed out that physicists know macroscopic sys- 
tems, such as superconductors, that behave quantum- 
mechanically.) A bucky ball is a molecule of sixty or seventy 
atoms of carbon arranged in a structure resembling a geo- 
desic dome. Buckminster Fuller made such domes famous, 
and the bucky ball is named after him. A molecule of sixty 
atoms is a relatively large entity, as compared with an atom. 
And yet, the same mysterious interference pattern appeared 
when Zeilinger and his colleagues ran their experiment. The 
arrangement is shown below. 




In each case, we see that the particles behave like waves. 
These experiments were also carried out one particle at a 
time, and still the interference pattern remained. What were 
these particles interfering with? The answer is that, in a sense, 
each particle went not through one slit, but rather through 
both slits — and then the particle "interfered with itself." 



THOMAS YOUNG'S EXPERIMENT & 2J 

What we are witnessing here is a manifestation of the quan- 
tum principle of superposition of states. 

The superposition principle says that a new state of a system 
may be composed from two or more states, in such a way that 
the new state shares some of the properties of each of the com- 
bined states. If A and B ascribe two different properties to a 
particle, such as being at two different places, then the super- 
position of states, written as A + B, has something in common 
both with state A and with state B. In particular, the particle 
will have non-zero probabilities for being in each of the two 
states, but not elsewhere, if the position of the particle is to be 
observed. 

In the case of the double-slit experiment, the experimental 
setup provides the particle with a particular kind of super- 
position: The particle is in state A when it passes through slit 
A and in state B when it passes through slit B. The superpo- 
sition of states is a combination of "particle goes through slit 
A" with "particle goes through slit B." This superposition 
of states is written as A + B. The two paths are combined, 
and there are therefore two nonzero probabilities, if the par- 
ticle is observed. Given that the particle is to be observed as 
it goes through the experimental setup, it will have a 50% 
chance of being observed to go through slit A and a 50% 
chance that it will be observed to go through slit B. But if the 
particle is not observed as it goes through the experimental 
setup, only at the end as it collects on the screen, the super- 
position holds through to the end. In a sense, then, the par- 
ticle has gone through both slits, and as it arrived at the end 
of the experimental setup, it interfered with itself. Superpo- 



26 C® ENTANGLEMENT 

sition of states is the greatest mystery in quantum mechanics. 
The superposition principle encompasses within itself the 
idea of entanglement. 

WHAT IS ENTANGLEMENT? 

Entanglement is an application of the superposition principle 
to a composite system consisting of two (or more) subsys- 
tems. A subsystem here is a single particle. Let's see what it 
means when we say that the two particles are entangled. Sup- 
pose that particle 1 can be in one of two states, A or C, and 
that these states represent two contradictory properties, such 
as being at two different places. Particle 2, on the other hand, 
can be in one of two states, B or D. Again these states could 
represent contradictory properties such as being at two dif- 
ferent places. The state AB is called a product state. When the 
entire system is in state AB, we know that particle 1 is in 
state A and particle 2 is in state B. Similarly, the state CD for 
the entire system means that particle 1 is in state C and par- 
ticle 2 is in state D. Now consider the state AB + CD. We 
obtain this state by applying the superposition principle to 
the entire, two-particle system. The superposition principle 
allows the system to be in such a combination of states, and 
the state AB + CD for the entire system is called an entangled 
state. While the product state AB (and similarly CD) ascribes 
definite properties to particles 1 and 2 (meaning, for exam- 
ple, that particle 1 is in location A and particle 2 is in loca- 
tion B), the entangled state — since it constitutes a 
superposition — does not. It only says that there are possibil- 
ities concerning particles 1 and 2 that are correlated, in the 
sense that if measurements are made, then if particle 1 is 



THOMAS YOUNG'S EXPERIMENT & 2J 

found in state A, particle 2 must be in state B; and similarly 
if particle 1 is in state C, then particle 2 will be in state D. 
Roughly speaking, when particles 1 and 2 are entangled, 
there is no way to characterize either one of them by itself 
without referring to the other as well. This is so even though 
we can refer to each particle alone when the two are in the 
product state AB or CD, but not when they are in the super- 
position AB + CD. It is the superposition of the two product 
states that produces the entanglement. 



This Page Intentionally Left Blank 



Planck's Constant 



"Planck had put forward a new, previously unimagined 
thought, the thought of the atomistic structure of energy." 

— Albert Einstein 



The quantum theory, with its bizarre consequences, 
was born in the year 1900, thirty-five years before 
Einstein and his colleagues raised their question 
about entanglement. The birth of the quantum theory is 
attributed to the work of a unique individual, Max Planck. 
Max Planck was born in Kiel, Germany, in 1858. He came 
from a long line of pastors, jurists, and scholars. His grand- 
father and great grandfather were both theology professors 
at the University of Gottingen. Planck's father, Wilhelm J. J. 
Planck, was a professor of Law in Kiel, and inspired in his 
son a deep sense of knowledge and learning. Max was his 
sixth child. Max's mother came from a long line of pastors. 
The family was wealthy and vacationed every year on the 
shores of the Baltic Sea and traveled through Italy and Aus- 
tria. The family was liberal in its views and, unlike many 



29 



30 C® ENTANGLEMENT 

Germans of the time, opposed Bismarck's politics. Max 
Planck saw himself as even more liberal than his family. 

As a student, Max was good but not excellent — he was 
never at the top of his class although his grades were gener- 
ally satisfactory. He exhibited a talent for languages, history, 
music, and mathematics, but never cared much for, nor 
excelled in, physics. He was a conscientious student and 
worked hard, but did not exhibit great genius. Planck was a 
slow, methodical thinker, not one with quick answers. Once 
he started working on something he found it hard to leave 
the subject and move on to something else. He was more a 
plodder than a naturally gifted intellect at the gymnasium. He 
often said that, unfortunately, he had not been given the gift 
of reacting quickly to intellectual stimulation. And he was 
always surprised that others could pursue several lines of 
intellectual work. He was shy, but was always well-liked by 
his teachers and fellow students. He saw himself as a moral 
person, one loyal to duties, perfectly honest, and pure of con- 
science. A teacher at the gymnasium encouraged him to pur- 
sue the harmonious interplay that he thought existed between 
mathematics and the laws of nature. This prompted Max 
Planck to study physics, which he did upon entering the Uni- 
versity of Munich. 

In 1878, Planck chose thermodynamics as the topic for his 
dissertation, which he completed in 1879. The thesis dealt 
with two principles of classical thermodynamics: the conser- 
vation of energy, and the increase of entropy with time, 
which characterize all observable physical processes. Planck 
extracted some concrete results from the principles of ther- 
modynamics and added an important premise: A stable equi- 



planck's constant c® 31 

librium is obtained at a point of maximum entropy. He 
emphasized that thermodynamics can produce good results 
without any reliance whatever on the atomic hypothesis. 
Thus a system could be studied based on its macroscopic 
properties without the scientist having to worry about what 
happens or doesn't happen to the system's tiny components: 
atoms, molecules, electrons, and so on. 

Thermodynamic principles are still extremely important in 
physics as they deal with the energy of entire systems. These 
principles can be used to determine the output of an internal 
combustion engine, for example, and have wide applicabil- 
ity in engineering and other areas. Energy and entropy are 
key concepts in physics, so one would have thought that 
Planck's work would have been well-received at the time. 
But it wasn't. Professors at Munich, and Berlin — where 
Planck had studied for a year — were not impressed by his 
work. They did not think the work was important enough to 
merit praise or recognition. One professor evaded Planck so 
he could not even serve him with a copy of his doctoral work 
when preparing for its defense. Eventually Planck was 
awarded the degree and was fortunate enough to obtain the 
position of associate professor at the University of Kiel, 
where his father still had a number of friends who could help 
him. He took his position in 1885 and immediately 
attempted to vindicate both his own work and thermody- 
namics as a whole. He entered a competition organized by 
the University of Gottingen to define the nature of energy. 
Planck's essay won second place — there was no first place. 
He soon realized that he would have had first place had not 
his article been critical of one of the professors at Gottingen. 



^Z co ENTANGLEMENT 

Nonetheless, his award impressed the physics professors at 
the University of Berlin, and they offered him a post of asso- 
ciate professor in their faculty in 1889. 

In time, the world of theoretical physics came to appreci- 
ate the principles of thermodynamics with their treatment of 
the concepts of energy and entropy, and Planck's work 
became more popular. His colleagues in Berlin, in fact, bor- 
rowed his dissertation so frequently that within a short time 
the manuscript started falling apart. In 1892 Planck was pro- 
moted to full professor in Berlin and in 1894 he became a full 
member of the Berlin Academy of Sciences. 

By the late 1800s, physics was considered a completed disci- 
pline, within which all explanations for phenomena and 
experimental outcomes had already been satisfactorily given. 
There was mechanics, the theory started by Galileo with his 
reputed experiment of dropping items from atop the Leaning 
Tower of Pisa, and perfected by the genius of Isaac Newton 
by the turn of the eighteenth century, almost two centuries 
before Planck's time. Mechanics and the theory of gravitation 
that goes with it attempt to explain the motions of objects of 
the size we see in everyday life up to the size of planets and 
the moon. It explains how objects move; that force is the 
product of mass and acceleration; the idea that moving 
objects have inertia; and that the earth exerts a gravitational 
pull on all objects. Newton taught us that the moon's orbit 
around the earth is in fact a constant "falling" of the moon 
down to earth, impelled by the gravitational pull both masses 
exert on each other. 

Physics also included the theory of electricity and electro- 



planck's constant c® 33 

magnetism developed by Ampere, Faraday, and Maxwell. 
This theory incorporated the idea of a field — a magnetic or 
electric field that cannot be seen or heard or felt, but which 
exerts its influence on objects. Maxwell developed equations 
that accurately described the electromagnetic field. He con- 
cluded that light waves are waves of the electromagnetic field. 
In 1831 Faraday constructed the first dynamo, which pro- 
duced electricity through the principle of electromagnetic 
inductance. By rotating a copper disc between two poles of 
an electromagnet, he was able to produce current. 

In 1887, during Planck's formative years, Heinrich Rudolf 
Hertz (1857-1894) conducted his experiments that produced 
radio waves. By chance, he noticed that a piece of zinc illu- 
minated by ultraviolet light became electrically charged. 
Without knowing it, he had discovered the photoelectric 
effect, which links light with matter. Around the same time, 
Ludwig Boltzmann (1844-1906) assumed that gases consist 
of molecules and treated their behavior using statistical meth- 
ods. In 1897, one °f tne most important discoveries of sci- 
ence took place: the existence of the electron was deduced by 
J. J. Thomson. 

Energy was a crucial idea within all of these various parts 
of classical physics. In mechanics, half the mass times the 
velocity squared was defined as a measure of kinetic energy 
(from the Greek word kinesis^ motion); there was another 
kind of energy, called potential energy. A rock on a high cliff 
possesses potential energy, which could then be instantly con- 
verted into kinetic energy once the rock is pushed slightly 
and falls from the cliff. Heat is energy, as we learn in high 
school physics. Entropy is a quality related to randomness 



34 ° ENTANGLEMENT 

and since randomness always increases, we have the law of 
increasing entropy — as everyone who has tried to put away 
toys knows well. 

So there was every reason for the world of physics to 
accept Planck's modest contributions to the theories of 
energy and entropy, and this was indeed what happened in 
Germany toward the end of the nineteenth century. Planck 
was recognized for his work in thermodynamics, and became 
a professor at the University of Berlin. During that time, he 
started to work on an interesting problem. It had to do with 
what is known as black-body radiation. Logical reasoning 
along the lines of classical physics led to the conclusion that 
radiation from a hot object would be very bright at the blue 
or violet end of the spectrum. Thus a log in a fireplace, glow- 
ing red, would end up emitting ultraviolet rays as well as x- 
rays and gamma rays. But this phenomenon, known as the 
ultraviolet catastrophe, doesn't really take place in nature. 
No one knew how to explain this odd fact, since the theory 
did predict this buildup of energy levels of radiation. On 
December 14, 1900, Max Planck presented a paper at a 
meeting of the German Physical Society. Planck's conclusions 
were so puzzling that he himself found it hard to believe 
them. But these conclusions were the only logical explanation 
to the fact that the ultraviolet catastrophe does not occur. 
Planck's thesis was that energy levels are quantized. Energy 
does not grow or diminish continuously, but is rather always 
a multiple of a basic quantum, a quantity Planck denoted as 
bv, where vis a characteristic frequency of the system being 
considered, and h is a fundamental constant now known as 
Planck's constant. (The value of Planck's constant is 
6.6262X10" 34 joule-seconds.) 



planck's constant & 35 

The Rayleigh-Jeans law of classical physics implied that the 
brightness of the black-body radiation would be unlimited at 
the extreme ultraviolet end of the spectrum, thus producing 
the ultraviolet catastrophe. But nature did not behave this way. 

According to nineteenth century physics (the work of 
Maxwell and Hertz), an oscillating charge produces radia- 
tion. The frequency (the inverse of the wavelength) of this 
oscillating charge is denoted by v, and its energy is £. Planck 
proposed a formula for the energy levels of a Maxwell-Hertz 
oscillator based on his constant b. The formula is: 

E=0, bv, 2b v, 3b v, 4b v . . . , or in general, nbv, where n is a non- 
negative integer. 

Planck's formula worked like magic. It managed to explain 
energy and radiation within a black body cavity in perfect 
agreement with the energy curves physicists were obtaining 
through their experiments. The reason for this was that the 
energy was now seen as coming in discrete packages, some 
large and some small, depending on the frequency of oscil- 
lation. But now, when the allotted energy for an oscillator 
(derived by other means) was smaller than the size of the 
package of energy available through Planck's formula, the 
intensity of the radiation dropped, rather than increasing to 
the high levels of the ultraviolet catastrophe. 

Planck had invoked the quantum. From that moment on, 
physics was never the same. Over the following decades, 
many confirmations were obtained that the quantum is 
indeed a real concept, and that nature really works this way, 
at least in the micro-world of atoms, molecules, electrons, 
neutrons, photons and the like. 



3 6 o ENTANGLEMENT 

Planck himself remained somewhat baffled by his own dis- 
covery. It is possible that he never quite understood it on a 
philosophical level. The trick worked, and the equations fit 
the data, but the question: "Why the quantum?" was one 
that not only he, but generations of future physicists and 
philosophers would ask and continue asking. 

Planck was a patriotic German who believed in German sci- 
ence. He was instrumental in bringing Albert Einstein to 
Berlin in 1914 and in promoting Einstein's election to the 
Prussian Academy of Sciences. When Hitler came to power, 
Planck tried to persuade him to change his decision to termi- 
nate the positions of Jewish academics. But Planck never quit 
his own position in protest, as some non-Jewish academics 
did. He remained in Germany, and throughout his life con- 
tinued to believe in promoting science in his homeland. 

Planck died in 1947. By that time, the quantum theory had 
matured and undergone significant growth to become the 
accepted theory of physical law in the world of the very 
small. Planck himself, whose work and discovery of quanta 
had initiated the revolution in science, never quite accepted 
it completely in his own mind. He seemed to be puzzled by 
the discoveries he had made, and at heart always remained a 
classical physicist, in the sense that he did not participate 
much in the scientific revolution that he had started. But the 
world of science moved forward with tremendous impetus. 



The Copenhagen School 



"The discovery of the quantum of action shows us not only 
the natural limitation of classical physics, but, by throwing 
a new light upon the old philosophical problem of the 
objective existence of phenomena independently of our 
observations, confronts us with a situation hitherto 
unknown in natural science." 

— Niels Bohr 



Niels Bohr was born in Copenhagen in 1885, in a six- 
teenth-century palace situated across the street from 
the Danish Parliament. The impressive building was 
owned by a succession of wealthy and famous people, includ- 
ing, two decades after Bohr's birth, King George I of Greece. 
The palace was bought by David Adler, Niels's maternal 
grandfather, a banker and member of the Danish Parliament. 
Bohr's mother, Ellen Adler, came from an Anglo-Jewish fam- 
ily that had settled in Denmark. On his father's side, Niels 
belonged to a family that had lived in Denmark for many 
generations, emigrating there in the late 1700s from the 
Grand Duchy of Mecklenburg in the Danish-speaking part of 
Germany. Niels's father, Christian Bohr, was a physician and 
scientist who was nominated for the Nobel Prize for his 
research on respiration. 



37 



ENTANGLEMENT 



David Adler also owned a country estate about ten miles 
from Copenhagen, and Niels was raised in very comfortable 
surroundings both in the city and in the country. Niels 
attended school in Copenhagen and was nicknamed "the fat 
one," since he was a large boy who frequently wrestled with 
his friends. He was a good student, although not the first in 
his class. 

Bohr's parents allowed their children to develop their gifts 
to the fullest. Bohr's younger brother, Harald, always showed 
a propensity for mathematics, and, in time, became a promi- 
nent mathematician. Niels stood out as a curious investiga- 
tor even as a very young child. While still a student, Niels 
Bohr undertook a project to investigate the surface tension of 
water by observing the vibrations of a spout. The project was 
planned and executed so well that it won him a gold medal 
from the Danish Academy of Sciences. 

At the university, Bohr was particularly influenced by Pro- 
fessor Christian Christiansen, who was the eminent Danish 
physicist of the time. The professor and the student had a 
relationship of mutual admiration. Bohr later wrote that he 
was especially fortunate to have come under the guidance of 
Christiansen, "a profoundly original and highly endowed 
physicist." Christiansen, in turn, wrote Bohr in 1916: "I have 
never met anybody like you who went to the bottom of 
everything and also had the energy to pursue it to comple- 
tion, and who in addition was so interested in life as a 
whole." 4 

Bohr was also influenced by the work of the leading Dan- 
ish philosopher, Harald Hoffding. Bohr had known Hoffding 
long before coming to the university, since he was a friend of 



THE COPENHAGEN SCHOOL & 39 

Bohr's father. Hoffding and other Danish intellectuals regu- 
larly met at the Bohr mansion for discussions, and Christian 
Bohr allowed his two sons, Niels and Harald, to listen to the 
discussions. Hoffding later became very interested in the 
philosophical implications of the quantum theory, developed 
by Niels Bohr. Some have suggested that, in turn, Bohr's for- 
mulation of the quantum principle of complementarity (dis- 
cussed later) was influenced by the philosophy of Hoffding. 

Bohr continued on to his Ph.D. in physics at the university, 
and in 1911 wrote his thesis on the electron theory of met- 
als. In his model, metals are viewed as a gas of electrons mov- 
ing more or less freely within the potential created by the 
positive charges in the metal. These positive charges are the 
nuclei of the atoms of the metal, arranged in a lattice. The 
theory could not explain everything, and its limitations were 
due to the application of classical — rather than the nascent 
quantum — ideas to the behavior of these electrons in a metal. 
His model worked so well that his dissertation defense 
attracted much attention and the room was full to capacity. 
Professor Christiansen presided over the proceedings. He 
remarked that it was unfortunate that the thesis had not been 
translated into a foreign language as well, since few Danes 
could understand the physics. Bohr later sent copies of his 
thesis to a number of leading physicists whose works he had 
made reference to in the thesis, including Max Planck. Unfor- 
tunately few responded, since none could understand Danish. 
In 1920, Bohr made an effort to translate the thesis into 
English, but never completed the project. 

Having finished his work, Bohr went to England on a 
postdoctoral fellowship supported by the Danish Carlsberg 



40 C® ENTANGLEMENT 

Foundation. He spent a year under the direction of J.J. 
Thomson at the Cavendish laboratory in Cambridge. The 
Cavendish laboratory was among the world's leading cen- 
ters for experimental physics, and its directors before Thom- 
son were Maxwell and Rayleigh. The laboratory has 
produced some twenty-odd Nobel laureates over the years. 

Thomson, who had won the Nobel Prize in 1906 for his 
discovery of the electron, was very ambitious. Often the film 
taken during experiments had to be hidden from him so he 
wouldn't snatch it before it was dry to inspect it, leaving fin- 
gerprints that blurred the pictures. He was on a crusade to 
rewrite physics in terms of the electron, and to push beyond 
the impressive work of his predecessor, Maxwell. 

Bohr worked hard in the laboratory, but often had diffi- 
culties blowing glass to make special equipment. He broke 
tubes, and fumbled in the unfamiliar language. He tried to 
improve his English by reading Dickens, using his dictionary 
for every other word. Additionally, Thomson was not easy to 
work with. The project Thomson assigned to Bohr had to 
do with cathode ray tubes, and was a dead end that did not 
yield any results. Bohr found an error in Thomson's calcula- 
tions, but Thomson was not one who could accept criticism. 
He was uninterested in being corrected, and Bohr — with his 
poor English — did not make himself understood. 

In Cambridge, Bohr met Lord James Rutherford (1871- 
1 937)? wno was recognized for his pioneering work on radi- 
ation, the discovery of the nucleus, and a model of the atom. 
Bohr was interested in moving to Manchester to work with 
Rutherford, whose theories had not yet received widespread 
acceptance. Rutherford welcomed him but suggested that he 



THE COPENHAGEN SCHOOL & 41 

first obtain Thomson's permission to leave. Thomson — who 
was not a believer in Rutherford's theory of the nucleus — 
was more than happy to let Bohr go. 

In Manchester, Bohr began the studies that would eventu- 
ally bring him fame. He started to analyze the properties of 
atoms in light of Rutherford's theory. Rutherford set Bohr to 
work on the experimental problem of analyzing the absorp- 
tion of alpha particles in aluminum. Bohr worked in the lab 
many hours a day, and Rutherford visited him and the rest of 
his students often, showing much interest in their work. After 
a while, however, Bohr approached Rutherford and said that 
he would rather do theoretical physics. Rutherford agreed 
and Bohr stayed home, doing research with pencil and paper 
and rarely coming into the lab. He was happy not to have to 
see anyone, he later said, as "no one there knew much." 

Bohr worked with electrons and alpha particles in his 
research, and produced a model to describe the phenomena 
that he and the experimental physicists were observing. The 
classical theory did not work, so Bohr took a big step: He 
applied quantum constraints to his particles. Bohr used 
Planck's constant in two ways in his famous theory of the 
hydrogen atom. First, he noted that the angular momentum of 
the orbiting electron in his model of the hydrogen atom had 
the same dimensions as Planck's constant. This led him to pos- 
tulate that the angular momentum of the orbiting electron 
must be a multiple of Planck's constant divided by zk, that is: 

mvr- h/2n, 2(h/2n), 3(h/2n), . . . 

Where the expression on the left is the classical definition of 
angular momentum (m is mass, v is speed, and r is the radius 



42 Cs ENTANGLEMENT 

of the orbit). This assumption of the quantizing of the angu- 
lar momentum led Bohr directly to quantizing the energy of 
the atom. 

Second, Bohr postulated that when the hydrogen atom 
drops from one energy level to a lower one, the energy that 
is released comes out as a single Einstein photon. As we will 
see later, the smallest quantity of energy in a light beam, 
according to Einstein, was hv, where h was Planck's constant 
and v the frequency, measured as the number of vibrations 
per second. With this development, and with his assumption 
of angular momentum, Bohr used Planck's quantum theory 
to explain what happens in the interior of an atom. This was 
a major breakthrough for physics. 

Bohr finished his paper on alpha particles and the atom 
after he left Manchester and returned to Copenhagen. The 
paper was published in 1913, marking the transition of his 
work to the quantum theory and the question of atomic 
structure. Bohr never forgot he was led to formulate his 
quantum theory of the atom from Rutherford's discovery of 
the nucleus. He later described Rutherford as a second father 
to him. 

Upon his return to Denmark, Bohr took up a position at 
the Danish Institute of Technology. He married Margrethe 
Norlund in 1912. She remained by his side throughout his 
life, and was a power in organizing the physics group 
founded in Copenhagen by her husband. 

On March 6, 1913, Bohr sent Rutherford the first chapter 
of his treatise on the constitution of atoms. He asked his for- 
mer mentor to forward the work to the Philosophical Mag- 
azine for publication. This manuscript was to catapult him 



THE COPENHAGEN SCHOOL & 43 

from a young physicist who has made some important 
progress in physics to a world figure in science. Bohr's break- 
through discovery was that it is impossible to describe the 
atom in classical terms, and that the answers to all questions 
about atomic phenomena had to come from the quantum 
theory. 

Bohr's efforts were aimed at first understanding the sim- 
plest atom of all, that of hydrogen. By the time he addressed 
the problem, physics had already learned that there are spe- 
cific series of frequencies at which the hydrogen atom radi- 
ates. These are the well-known series of Rydberg, Balmer, 
Lyman, Paschen, and Brackett — each covering a different 
part of the spectrum of radiation from excited hydrogen 
atoms, from ultraviolet through visible light to infrared. Bohr 
sought to find a formula that would explain why hydrogen 
radiates in these particular frequencies and not others. 

Bohr deduced from the data available on all series of radi- 
ation of hydrogen that every emitted frequency was due to 
an electron descending from one energy level in the atom to 
another, lower level. When the electron came down from 
one level to another, the difference between its beginning 
and ending energies was emitted in the form of a quantum 
of energy. There is a formula linking these energy levels and 
quanta: 

E a -E b =hv ab 

Where E a is the beginning energy level of the electron around 
the hydrogen nucleus; E^ is the ending energy level once the 
electron has descended from its prior state; h is Planck's con- 
stant; and v a b is the frequency of the light quantum emitted 



44 ° ENTANGLEMENT 

during the electron's jump down from the first to the second 
energy level. This is demonstrated by the figure below. 




Rutherford's simple model of the atom did not square well 
with reality. Rutherford's atom was modeled according to 
classical physics, and if the atom was as simple as the model 
implied, it would not have existed for more than one-hun- 
dred-millionth of a second. Bohr's tremendous discovery of 
the use of Planck's constant within the framework of the 
atom solved the problem beautifully. The quantum theory 
now explained all observed radiation phenomena about 
hydrogen, which had until then baffled physicists for 
decades. 

Bohr's work has been partially extended to explain the 
orbits and energies of electrons in other elements and to bring 
us understanding of the periodic table of the elements, chem- 
ical bonds, and other fundamental phenomena. The quan- 
tum theory had just been put to exceptionally good use. It 
was becoming obvious that classical physics would not work 



THE COPENHAGEN SCHOOL Ca> 4J 

well in the realm of atoms and molecules and electrons, and 
that the quantum theory was the correct path to take. 

Bohr's brilliant solution to the question of the various 
series of spectral lines of radiation for the hydrogen atom left 
unanswered the question: Why? Why does an electron jump 
from one energy level to another, and how does the electron 
know that it should do so? This is a question of causality. 
Causality is not explained by the quantum theory, and in fact 
cause and effect are blurred in the quantum world and have 
no explanation or meaning. This question about Bohr's work 
was raised by Rutherford as soon as he received Bohr's man- 
uscript. Also, the discoveries did not bring about a general 
formulation of quantum physics, applicable in principle to all 
situations and not just to special cases. This was the main 
question of the time, and the goal was not achieved until 
later, that is, until the birth of "the new quantum mechanics" 
with the work of de Broglie, Heisenberg, Schrodinger, and 
others. 

Bohr became very famous following his work on the quan- 
tum nature of the atom. He petitioned the Danish govern- 
ment to endow him with a chair of theoretical physics, and 
the government complied. Bohr was now Denmark's favorite 
son and the whole country honored him. Over the next few 
years he continued to travel to Manchester to work with 
Rutherford, and traveled to other locations and met many 
physicists. These connections allowed him to found his own 
institute. 

In 1918, Bohr secured permission from the Danish gov- 



46 & ENTANGLEMENT 

ernment to found his institute of theoretical physics. He 
received funding from the Royal Danish Academy of Science, 
which draws support from the Carlsberg brewery. Bohr and 
his family moved into the mansion owned by the Carlsberg 
family on the premises of his new institute. Many young 
physicists from around the world regularly came to spend a 
year or two working at the institute and drawing their inspi- 
ration from the great Danish physicist. Bohr became close 
with the Danish royal family, as well as with many members 
of the nobility and the international elite. In 1922, he 
received the Nobel Prize for his work on the quantum theory. 
Bohr organized regular scientific meetings at his institute in 
Copenhagen, to which many of the world's greatest physi- 
cists came and discussed their ideas. Copenhagen thus 
became a world center for the study of quantum mechanics 
during the period the theory was growing: from its founding 
in the late first decade of the twentieth century until just 
before the Second World War. The scientists who worked at 
the institute (to be named the Niels Bohr Institute after its 
founder's death), and many who came to attend its meetings, 
later developed what is called the Copenhagen Interpreta- 
tion of the quantum theory, often called the orthodox inter- 
pretation. This was done after the birth of the "new quantum 
mechanics" in the middle 1920s. According to the Copen- 
hagen interpretation of the rules of the quantum world, there 
is a clear distinction between what is observed and what is 
not observed. The quantum system is submicroscopic and 
does not include the measuring devices or the measuring 
process. In the years to come, the Copenhagen interpretation 



THE COPENHAGEN SCHOOL Ca> 4J 

would be challenged by newer views of the world brought 
about by the maturing of the quantum theory. 

Starting in the 1920s, and culminating in 1935, a major 
debate would rage within the community of quantum physi- 
cists. The challenge would be issued by Einstein, and 
throughout the rest of his life, Bohr would regularly spar 
with Einstein on the meaning and completeness of the quan- 
tum theory. 



This Page Intentionally Left Blank 



6 

De Broglie' s Pilot Waves 



"After long reflection in solitude and meditation, I suddenly 
had the idea, during the year 1923, that the discovery made 
by Einstein in 1905 should be generalized by extending it 
to all material particles and notably to electrons." 

— Louis de Broglie 



Duke Louis Victor de Broglie was born in Dieppe in 
I 1892 to an aristocratic French family that had long 
provided France with diplomats, politicians, and 
military leaders. Louis was the youngest of five children. His 
family expected Louis' adored older bother, Maurice, to enter 
the military service, and so Louis too decided to serve France. 
He chose the navy, since he thought it might allow him to 
study the natural sciences, which had fascinated him since 
childhood. He did indeed get to practice science by installing 
the first French wireless transmitter aboard a ship. 

After Maurice left the military and studied in Toulon and 
at the University of Marseilles, he moved to a mansion in 
Paris, where in one of the rooms he established a laboratory 
for the study of X-rays. To aid him in his experiments, the 
resourceful Maurice trained his valet in the rudiments of sci- 



49 



JO C© ENTANGLEMENT 

entific procedure, and eventually converted his personal ser- 
vant into a professional lab assistant. His fascination with 
science was infectious. Soon, his younger brother Louis was 
also interested in the research and helped him with 
experiments. 

Louis attended the Sorbonne, studying medieval history. 
In 1911, Maurice served as the secretary of the famous 
Solvay Conference in Brussels, where Einstein and other lead- 
ing physicists met to discuss the exciting new discoveries in 
physics. Upon his return, he regaled his younger brother with 
stories about the fascinating discoveries, and Louis became 
even more excited about physics. 

Soon, World War I erupted and Louis de Broglie enlisted in 
the French army. He served in a radio communication unit, 
a novelty at that time. During his service with the radio-teleg- 
raphy unit stationed at the top of the Eiffel Tower, he learned 
much about radio waves. And indeed he was to make his 
mark on the world through the study of waves. When the 
war ended, de Broglie returned to the university and studied 
under some of France's best physicists and mathematicians, 
including Paul Langevin and Emile Borel. He designed exper- 
iments on waves and tested them out at his brother's labo- 
ratory in the family's mansion. De Broglie was also a lover of 
chamber music, and so he had an intimate knowledge of 
waves from a music-theory point of view. 

De Broglie immersed himself in the study of the proceed- 
ings of the Solvay Conference given to him by his brother. He 
was taken by the nascent quantum theory discussed in 1911 
and repeatedly presented at later Solvay meetings throughout 
the following years. De Broglie studied ideal gases, which 



DE BROGLIE'S PILOT WAVES & $1 

were discussed at the Solvay meeting, and came to a suc- 
cessful implementation of the theory of waves in analyzing 
the physics of such gases, using the quantum theory. 

In 1923, while working for a doctorate in physics in Paris, 
"all of a sudden," as he later put it, "I saw that the crisis in 
optics was simply due to a failure to understand the true uni- 
versal duality of wave and particle." At that moment, in fact, 
de Broglie discovered this duality. He published three short 
notes on the topic, hypothesizing that particles were also 
waves and waves also particles, in the Proceedings of the 
Paris Academy in September and October 1923. He elabo- 
rated on this work and presented his entire discovery in his 
doctoral dissertation, which he defended on November 25, 
1924. 

De Broglie took Bohr's conception of an atom and 
viewed it as a musical instrument that can emit a basic tone 
and a sequence of overtones. He suggested that all parti- 
cles have this kind of wave-aspect to them. He later 
described his efforts: "I wished to represent to myself the 
union of waves and particles in a concrete fashion, the par- 
ticle being a little localized object incorporated in the struc- 
ture of a propagating wave." Waves that he associated with 
particles, de Broglie named pilot waves. Every small parti- 
cle in the universe is thus associated with a wave propa- 
gating through space. 

De Broglie derived some mathematical concepts for his 
pilot waves. Through a derivation using several formulas and 
Planck's quantum-theory constant, b, de Broglie came up 
with the equation that is his legacy to science. His equation 
links the momentum of a particle, p, with the wavelength of 



J2 & ENTANGLEMENT 

its associated pilot wave, A, through an equation using 
Planck's constant. The relationship is very simply stated as: 

p=h/X 

De Broglie had a brilliant idea. Here, he was using the 
machinery of the quantum theory to state a very explicit rela- 
tionship between particles and waves. A particle has momen- 
tum (classically, the product of its velocity and its mass). 
Now this momentum was directly linked with the wave asso- 
ciated with the particle. Thus a particle's momentum in 
quantum mechanics is, by de Broglie's formula, equal to the 
quotient of Planck's constant and the wavelength of the wave 
when we view the particle as a wave. 

De Broglie did not provide an equation to describe the 
propagation of the wave associated with a particle. That task 
would be left to another great mind, Erwin Schrodinger. For 
his pioneering work, de Broglie received the Nobel Prize after 
many experiments verified the wave nature of particles over 
the following years. 

De Broglie remained active as a physicist and lived a long 
life, dying in 1987 at the age of 95. When de Broglie was 
already a world-famous scientist, the physicist George 
Gamow (who wrote Thirty Years that Shook Physics) visited 
him in his mansion in Paris. Gamow rang the bell at the gate 
of the estate and was greeted by de Broglie's butler. He said: 
"Je voudrais voir Professeur de Broglie." The butler cringed. 
"Vous voulez dire, Monsieur le Due de Broglie!" he insisted. 
"O.K., le Due de Broglie," Gamow said and was finally 
allowed to enter. 



DE BROGLIE'S PILOT WAVES Ca> 53 



Are particles also waves? Are waves also particles? The 
answer the quantum theory gives us is "Yes." A key charac- 
teristic of a quantum system is that a particle is also a wave, 
and exhibits wave interference characteristics when passed 
through a double-slit experimental setup. Similarly, waves can 
be particles, as Einstein has taught us when he developed his 
photoelectric effect Nobel Prize-winning paper, which will be 
described later. Light waves are also particles, called photons. 

Laser light is coherent light, in which all the light waves are 
in phase; hence the power of lasers. In 2001, the Nobel Prize 
in physics was shared by three scientists who showed that 
atoms, too, can behave like light rays in the sense that an 
ensemble of them can all be in a coherent state, just like laser 
light. This proved a conjecture put forth by Einstein and his 
colleague, the Indian physicist Saryendra Nath Bose, in the 
1920s. Bose was an unknown professor of physics at the Uni- 
versity of Dacca, and in 1924 he wrote Einstein a letter in 
which he described how Einstein's light quanta, the photons, 
could form a kind of "gas," similar to the one consisting of 
atoms or molecules. Einstein rewrote and improved Bose's 
paper and submitted it for joint publication. This gas pro- 
posed by Bose and Einstein was a new form of matter, in 
which individual particles did not have any properties and 
were not distinguishable. The Bose-Einstein new form of 
matter led Einstein to a "hypothesis about an interaction 
between molecules of an as yet quite mysterious nature." 

The Bose-Einstein statistics allowed Einstein to make 
groundbreaking predictions about the behavior of matter at 



J4 ® ENTANGLEMENT 

extremely low temperatures. At such low temperatures, vis- 
cosity of liquefied gases disappears, resulting in superfluidity. 
The process is called Bose-Einstein condensation. 

Louis de Broglie had submitted his doctoral dissertation 
to Einstein's friend in Paris, Paul Langevin, in 1924. Langevin 
was so impressed with de Broglie's idea that matter can have 
a wave aspect, that he sent the thesis to Einstein, asking for 
his opinion. When Einstein read de Broglie's thesis he called 
it "very remarkable," and he later used the de Broglie wave 
idea to deduce the wave properties of the new form of mat- 
ter he and Bose had discovered. But no one had seen a Bose- 
Einatein condensate . . . until 1995. 

On June 5, 1995, Carl Weiman of the University of Col- 
orado and Eric Cornell of the National Institute of Standards 
and Technology used high-powered lasers and a new tech- 
nique for cooling matter to close to absolute zero to super- 
cool about 2000 atoms of rubidium. These atoms were found 
to possess the qualities of a Bose-Einstein condensate. They 
appeared as a tiny dark cloud, in which the atoms themselves 
had lost their individuality and entered a single energy state. 
For all purposes, these atoms were now one quantum entity, 
as characterized by their de Broglie wave. Shortly afterwards, 
Wolfgang Ketterle of M.I.T. reproduced the results and 
improved the experiment, producing what was the equivalent 
of a laser beam made of atoms. For their work, the three sci- 
entists shared the 2001 Nobel Prize in Physics, and de 
Broglie's fascinating idea was reconfirmed in a new setting 
that pushed the limits of quantum mechanics up the scale 
toward macroscopic objects. 



7 

Schrodinger and His Equation 



"Entanglement is not one but rather the characteristic trait 
of quantum mechanics." 

— Erwin Schrodinger 



Erwin Schrodinger was born in a house in the center 
of Vienna in 1887 to well-to-do parents. An only 
child, he was doted on by several aunts, one of 
whom taught him to speak and read English before he even 
mastered his native German. As a young boy, Erwin started 
to keep a journal, a practice he maintained throughout his 
life. From an early age, he exhibited a healthy skepticism and 
tended to question things that people presented as facts. 
These two habits were very useful in the life of a scientist 
who would make one of the most important contributions to 
the new quantum theory. Questioning what from our every- 
day life we take as truth is essential in approaching the world 
of the very small. And Schrodinger's notebooks would be 
crucial in his development of the wave equation. 

At age eleven, Erwin entered the gymnasium located a few 



55 



j6 & ENTANGLEMENT 

minutes' walk from his house. In addition to mathematics 
and the sciences, the gymnasium taught its students Greek 
language and culture, Latin, and the classic works of antiq- 
uity, including Ovid, Livy, Cicero, and Homer. Erwin loved 
mathematics and physics, and excelled in them, solving prob- 
lems with an ease and facility that stunned his peers. But he 
also enjoyed German poetry and the logic of grammar, both 
ancient and modern. This logic, in mathematics and in 
humanistic studies, shaped his thinking and prepared him 
for the rigors of the university. 

Erwin loved hiking, mountaineering, the theater, and pretty 
girls — amusements that would mark his behavior throughout 
his life. As a young boy, he worked hard at school, but also 
played hard. He spent many days walking in the mountains, 
reading mathematics, and courting his best friend's sister, a 
dark-haired beauty named Lotte Rella. 5 

In 1906, Schrodinger enrolled at the University of 
Vienna — one of the oldest in Europe, established in 1365 — 
to study physics. There was a long legacy of physics at the 
university. Some of the great minds that had worked there 
and left about the time Schrodinger enrolled were Ludwig 
Boltzmann, the proponent of the atomic theory, and Ernst 
Mach, the theoretician whose work inspired Einstein. There 
Schrodinger was a student of Franz Exner, and did work in 
experimental physics, some of it relating to radioactivity. The 
University of Vienna was an important center for the study 
of radioactivity, and Marie Curie in Paris received some of 
her specimens of radioactive material, with which she made 
her discoveries, from the physics department at Vienna. 

Schrodinger was admired by his fellow students for his 



SHRODINGER AND HIS EQUATION & jy 

brilliance in physics and mathematics. He was always sought 
out by his friends for help in mathematics. One of the sub- 
jects in mathematics that he took at the University of Vienna 
was differential equations, in which he excelled. As fate 
would have it, this special skill proved invaluable in his 
career: it helped him solve the biggest problem of his life and 
establish his name as a pioneer of quantum mechanics. 

But Schrodinger lived a multifacted life as a university stu- 
dent in Vienna at the height of its imperial glory. He retained 
his abilities as an athlete and was as highly social as he'd ever 
been: He found a number of good friends with whom he 
spent his free time climbing and hiking in the mountains. 
Once, in the Alps, he spent an entire night nursing a friend 
who had broken a leg while climbing. Once his friend was 
taken to the hospital, he spent the day skiing. 

In 1910, Schrodinger wrote his doctoral thesis in physics, 
entitled "On the conduction of electricity on the surface of 
insulators in moist air." This was a problem that had some 
implications in the study of radioactivity, but the thesis was 
not a brilliant work of scholarship. Schrodinger had left out 
a number of factors about which he should have known, and 
his analysis was neither complete nor ingenious. Still, the 
work was enough to earn him his doctorate, and following 
his graduation he spent a year in the mountains as a volun- 
teer in the fortress artillery. He then returned to the univer- 
sity to work as an assistant in a physics laboratory. 
Meanwhile, he labored on the required paper (called a Habil- 
itationschrift) that would allow him to earn income as a pri- 
vate tutor at the university. His paper, "On the Kinetic 
Theory of Magnetism," was a theoretical attempt to explain 



j8 C© ENTANGLEMENT 

the magnetic properties of various compounds, and was also 
not of exceptional quality, but it satisfied the requirements 
and allowed him to work at the university. His academic 
career had begun. 

Shortly afterwards, Schrodinger, who was now in his early 
twenties, met another teenage girl who caught his fancy. Her 
name was Felicie Krauss, and her family belonged to Aus- 
tria's lower nobility. The two developed a relationship and 
considered themselves engaged despite strong objections 
from the girl's parents. Felicie's mother, especially, was deter- 
mined not to allow her daughter to marry a working-class 
person; one who, she believed, would never be able to sup- 
port her daughter in an appropriate style on his university 
income. In despair, Erwin contemplated leaving the university 
and working for his father, who owned a factory. But the 
father would hear nothing of it, and with the mounting pres- 
sure from Felicie's mother, the two lovers called off their 
informal engagement. While she later married, Felicie always 
remained close to Erwin. This, too, was a pattern that con- 
tinued throughout Schrodinger's life: wherever he went — 
even after he was married — there were always young 
girlfriends never too far away. 

Schrodinger continued his study of radioactivity in the lab- 
oratory of the University of Vienna. In 1912, his colleague 
Victor Hess soared 16,000 feet in a balloon with instruments 
to measure radiation. He wanted to solve the problem of why 
radiation was detected not only close to the ground, where 
deposits of radium and uranium were its source, but also in 
the air. Up in his balloon, Hess discovered to his surprise that 
the radiation was actually three times as high as it was at 



SHRODINGER AND HIS EQUATION & 59 

ground level. Hess had thus discovered cosmic radiation, for 
which he later received the Nobel Prize. Schrodinger, taking 
part in related experiments on the background radiation at 
ground level, traveled throughout Austria with his own radi- 
ation-detecting instruments. This travel incidentally allowed 
him to enjoy his beloved outdoors — and make new friends. 
In 1913, he was taking radiation measurements in the open 
air in the area where a family he had known from Vienna 
was vacationing. With the family was a pretty teenage girl, 
Annemarie ("Anny") Bertel. The twenty-six year old scientist 
and the sixteen-year-old girl were attracted to each other, and 
through meetings over the next several years, developed a 
romance that resulted in marriage. Anny remained devoted 
to Schrodinger throughout his life, even tolerating his per- 
petual relationships with other women. 

In 1914, Schrodinger reenlisted in the fortress artillery to 
fight on the Italian front of World War I. Even in the field, he 
continued to work on problems of physics, publishing papers 
in professional journals. None of his papers thus far had been 
exceptional, but the topics were interesting. Schrodinger 
spent much time doing research on color theory, and made 
contributions to our understanding of light of different wave- 
lengths. During one of his experiments on color while still at 
the University of Vienna, Erwin discovered that his own color 
vision was deficient. 

In 1917, Schrodinger wrote his first paper on the quantum 
theory, on atomic and molecular heats. The research for this 
paper brought to his attention the work of Bohr, Planck, and 
Einstein. By the time the war was over, Schrodinger had 
addressed not only the quantum theory, but also Einstein's 



60 & ENTANGLEMENT 

theory of relativity. He had now brought himself into the 
leading edge of theoretical physics. 

In the years following the war, Schrodinger taught at uni- 
versities in Vienna, Jena, Breslau, Stuttgart, and Zurich. In 
1920, in Vienna, Erwin married Anny Bertel. Her income 
was higher than his university salary, which made him upset 
and prompted him to seek employment at other universities 
throughout Europe. Through Anny, Erwin met Hansi Bauer, 
who later became one of the girlfriends he would maintain 
throughout his life. 

In Stuttgart, in 1921, Schrodinger began a very serious 
effort to understand and further develop the quantum theory. 
Bohr and Einstein, who were not much older than 
Schrodinger, had already made their contributions to the 
theory while in their twenties. Schrodinger was getting older, 
and he still had not had a major scientific achievement. He 
concentrated his efforts on modeling the spectral lines of 
alkali metals. 

In late 1921, Schrodinger was nominated for a coveted 
position of full Professor of Theoretical Physics at the Uni- 
versity of Zurich. That year, he published his first important 
paper in the quantum area, about quantized orbits of a single 
electron, based on the earlier work of Bohr. Soon after his 
arrival in Zurich, however, he was diagnosed with pul- 
monary disease and his doctors ordered rest at high altitude. 
The Schrodingers decided on the village of Arosa in the Alps, 
not far from Davos, at an altitude of 6,000 feet. Upon his 
recovery, they returned to Zurich and there, in 1922, 
Schrodinger gave his inaugural lecture at the university. Dur- 
ing 1923 and 1924, Schrodinger's research was centered on 



SHRODINGER AND HIS EQUATION & 6l 

spectral theory, light, atomic theory, and the periodic nature 
of the elements. In 1924, at the age of 37, he was invited to 
attend the Solvay Conference in Brussels, where the greatest 
minds in physics, including Einstein and Bohr, met. 
Schrodinger was there almost as an outside observer, since he 
had not produced any earth-shattering papers. 

The quantum theory was nowhere near being complete, 
and Erwin Schrodinger was desperately seeking a topic in 
the quantum field with which he could make his mark. Time 
was running out on him, and if nothing happened soon, he 
would be condemned to obscurity, mediocrity, and to remain 
forever in the sidelines while others were making scientific 
history. In 1924, Peter Debye at the University of Zurich 
asked Schrodinger to report on de Broglie's thesis on the 
wave theory of particles at a seminar held at the university. 
Schrodinger read the paper, started thinking about its ideas, 
and decided to pursue them further. He worked on de 
Broglie's particle-wave notion for a full year, but made no 
breakthrough. 

A few days before Christmas, 1925, Erwin left for the 
Alps, to stay in the Villa Herwig in Arosa, where he and 
Anny had spent several months while he was recuperating 
four years earlier. This time he came without his wife. From 
his correspondence, we know that he had one of his former 
girlfriends from Vienna join him at the villa, and stay with 
him there till early 1926. Schrodinger's biographer Walter 
Moore makes much of the mystery as to who the girlfriend 
might have been. 6 Could she have been Lotte, Felicie, Hansi, 
or one of his other liaisons? At any rate, according to the 
physicist Hermann Weyl, Schrodinger's erotic encounters 



6l & ENTANGLEMENT 

with the mystery lady produced the burst of energy 
Schrodinger required to make his great breakthrough in the 
quantum theory. Over the Christmas vacation in the Alps 
with his secret lover, Schrodinger produced the now-famous 
Schrodinger equation. The Schrodinger equation is the math- 
ematical rule that describes the statistical behavior of parti- 
cles in the micro-world of quantum mechanics. The 
Schrodinger equation is a differential equation. 

Differential equations are mathematical equations that 
state a relationship between a quantity and its derivatives, 
that is, between a quantity and its rate of change. Velocity, 
for example, is the derivative (the rate of change) of loca- 
tion. If you are moving at sixty miles per hour, then your 
location on the road changes at a rate of sixty m.p.h. Accel- 
eration is the rate of change of velocity (when you accelerate, 
you are increasing the speed of your car); thus acceleration is 
the second derivative of location, since it is the rate of change 
of the rate of change of location. An equation that states your 
location, as a variable, as well as your velocity, is a differen- 
tial equation. An equation relating your location with your 
velocity and your acceleration is a second-order differential 
equation. 

By the time Schrodinger started to address the problem of 
deriving the equation that governs the quantum behavior of 
a small particle such as the electron, a number of differential 
equations of classical physics were known. For example, the 
equation that governs the progression of heat in a metal was 
known. Equations governing classical waves, for example, 
waves on a vibrating string, and sound waves, were already 
well known. Having taken courses in differential equations, 



SHRODINGER AND HIS EQUATION & 63 

Schrodinger was well aware of these developments. 
Schrodinger's task was to find an equation that would 
describe the progression of particle waves, the waves that de 
Broglie had associated with small particles. Schrodinger 
made some educated guesses about the form his equation 
must take, based on the known classical wave equation. 
What he had to determine, however, was whether to use the 
first or the second derivative of the wave with respect to loca- 
tion, and whether to use the first or the second derivative 
with respect to time. His breakthrough occurred when he 
discovered that the proper equation is first-order with respect 
to time and second-order with respect to location. 

m f =E¥ 

The above is the time-independent Schrodinger equation, 
stated in its simplest symbolic way. The symbol W represents 
the wave function of a particle. This is de Broglie's "pilot 
wave" of a particle. But here this is no longer some hypo- 
thetical entity, but rather a function that we can actually 
study and analyze using the Schrodinger equation. The sym- 
bol H stands for an operator, which is represented by a for- 
mula of its own, telling it what to do to the wave function: 
take a derivative and also multiply the wave function by 
some numbers, including Planck's constant, h. The operator 
H operates on the wave equation, and the result, on the other 
side of the equation, is an energy level, £, multiplied by the 
wave function. 

Schrodinger's equation has been applied very successfully 
to a number of situations in quantum physics. What a physi- 
cist does is to write the equation above, applied to a partic- 



64 & ENTANGLEMENT 

ular situation, say, a particle placed in a microscopic box, or 
an electron placed in a potential field, or the hydrogen atom. 
In each situation, the physicist then solves Schrodinger's 
equation, obtaining a solution. The solutions of the 
Schrodinger equation are waves. 

Waves are usually represented in physics by trigonometric 
functions, most often the sine and the cosine functions, 
whose graphs look just like the picture of a wave. (Physicists 
also use other functions, such as exponentials.) The picture 
below is a typical sine wave. 




A Sine Wave 

In solving the Schrodinger equation, a physicist will get a 
solution that states the wave function as something like: y ¥= 
A sin (nKx/L). (This is the solution for a particle in a rigid 
box. The term "sin" stands for the wave-like sine function, 
while all the other letters in the equation are constants or a 
variable (x). But the essential element here is the sine 
function.) 

With his wave equation, Schrodinger brought quantum 
mechanics to a very high level. Scientists could now deal with 
a concrete wave function, which they could sometimes write 
down in specific terms, as in the example above, to describe 
particles or photons. This brought quantum theory to a point 
where several of its most important aspects are evident. Two 
of these notions are probability and superposition. 



SHRODINGER AND HIS EQUATION & 6$ 

When we deal with quantum systems — each with an asso- 
ciated wave function *P — we no longer deal with precisely 
known elements. A quantum particle can only be described 
by its probabilities — never by exact terms. These probabili- 
ties are completely determined by the wave function, y V. The 
probabilistic interpretation of quantum mechanics was sug- 
gested by Max Born, although Einstein knew it first. The 
probability that a particle will be found in a given place is 
equal to the square of the amplitude of the wave function at 
that location: 

Probability^ I 2 

This is an extremely important formula in quantum theory. 
In many ways, it represents the essence of what quantum 
theory can give us. In classical physics, we can — in princi- 
ple — measure, determine, and predict the location and the 
speed of a moving object with 100% certainty. This feature 
of classical (large-scale) physics is what allows us, for exam- 
ple, to land a spacecraft on the moon, not to mention drive 
a car or answer the door. In the world of the very small, we 
do not have these abilities to predict movements of particu- 
lar objects. Our predictions are only statistical in their nature. 
We can determine where a particle will be (if the position 
observable is actualized) only in terms of probabilities of dif- 
ferent outcomes (or, equivalently, what proportion of a large 
number of particles will fall at a specific location). 
Schrodinger's equation allows us to make such probabilistic 
predictions. As would be proven mathematically within a 
few decades, probabilities are all that we can get from quan- 
tum mechanics. There are no hidden quantities here whose 



66 & ENTANGLEMENT 

knowledge would reduce the uncertainty. By its very nature, 
the quantum theory is probabilistic. 

Probabilities are given by a probability distribution, which 
in the case of quantum theory is specified by the square of the 
amplitude of the wave function. Predicting the outcomes of 
quantum events is different from predicting the motion of a 
car, for example, where if you know the speed and initial 
location of the car, you will know its location after a certain 
period of time driving at a given speed, when both time and 
speed can be measured to great accuracy. If you drive for two 
hours at 60 mph, you will be 120 miles away from where 
you started. In the quantum world this does not happen. The 
best you can do is to predict outcomes in terms of probabil- 
ities. The situation, therefore, is similar to rolling two dice. 
Each die has a probability of 1/6 of landing on any given 
number. The two dice are independent, so the probability of 
rolling two sixes is the product of the probability of rolling 
a six on one die, 1/6, and the probability of rolling a six on 
the other die, again 1/6. The probability of two sixes is there- 
fore 1/36. The probability of getting a sum of 12 on two dice 
is thus 1/36. The sum of two dice has the highest probabil- 
ity of equaling 7. That probability is 1/6. The distribution of 
the sum of two dice is shown below. 



SHRODINGER AND HIS EQUATION Ca> 6j 



. 6/36 
§ 5/36 



! 4/36 



CD 

< 
CO 

O 3/36 

cc 

a. 2/36 

1/36 



7 
SUM 



10 11 



12 



The square of the amplitude of the wave function, *P , is 
often a bell-shaped distribution. One such distribution is 
shown below. 



Density 




>X 



[i 



The distribution above gives us the probability of finding 
the particle in any given range of values of the horizontal 
axis by the area under the curve above that region. 

The second essential element of the quantum theory 
brought to light by Schrodinger's equation is the superposi- 
tion principle. Waves can always be superposed on one 
another. The reason for this is that the sine curve and the 
cosine curve for various parameters can be added to one 
another. This is the principle of Fourier analysis, discovered 



68 C© ENTANGLEMENT 

by the great French mathematician Joseph B. J. Fourier 
(1768-1830) and published in his book, Tbeorie analytique 
de la chaleur (Analytic Theory of Heat) in 1822. Fourier 
applied his theory to the propagation of heat, as suggested by 
the title of his book. He proved that many mathematical 
functions can be seen as the sum of many sine and cosine 
wave functions. 

In quantum mechanics, because the solutions of 
Schrodinger's equation are waves, sums of these waves are 
also solutions to the equation. (The sum of several solutions 
of the Schrodinger equation is a solution because of the prop- 
erty of linearity.) This suggests, for example, that the electron 
can also be found in a state that is a superposition of other 
states. This happens because a solution of Schrodinger's equa- 
tion for the electron would be some sine wave and thus a sum 
of such sine waves could also be a solution. 

The superposition of waves explains the phenomenon of 
interference. In Young's double-slit experiment, the waves 
interfere with each other: that is, the bright lines on the screen 
are regions where the waves from the two slits add up to 
reinforce each other, while the dark streaks are regions where 
they subtract from each other, making the light weaker or 
completely absent. 

Superposition is one of the most important principles in 
quantum mechanics. The weirdness of quantum mechanics 
really kicks in when a particle is superposed with itself. In 
Young's experiment, when the light is so weak that only one 
photon it emitted at a time, we still find the interference pat- 
tern on the screen. (The pattern is produced by many pho- 
tons, not one, even though only one photon arrives at a time.) 



SHRODINGER AND HIS EQUATION & 69 

The explanation for this phenomenon is that the single pho- 
ton does not choose one slit or the other to go through. It 
chooses both slits, that is, one slit and the other. The particle 
goes through both slits, and then it interferes with itself, as 
two waves do by superposition. 

When the quantum system contains more than one particle, 
the superposition principle gives rise to the phenomenon of 
entanglement. It is now not just a particle interfering with 
itself — it is a system interfering with itself: an entangled sys- 
tem. Amazingly enough, Erwin Schrodinger himself realized 
that particles or photons produced in a process that links them 
together will be entangled, and he actually coined the term 
entanglement, both in his native German and in English. 
Schrodinger discovered the possibility of entanglement in 1926, 
when he did his pioneering work on the new quantum mechan- 
ics, but he first used the term entanglement in 193 5, in his dis- 
cussion of the Einstein, Podolsky, and Rosen (EPR) paper. 

According to Home, Shimony, and Zeilinger, Schrodinger 
recognized in a series of papers in 1926 that the quantum 
state of an w-particle system can be entangled. 7 Schrodinger 
wrote: 

We have repeatedly drawn attention to the fact that the *F 
function itself cannot and may not be interpreted directly in 
terms of three-dimensional space — however much the one- 
electron problem tends to mislead us on this point — because it 
is in general a function in configuration space, not real space. 8 

According to Home, Shimony, and Zeilinger, Schrodinger 
thus understood that the wave function in configuration 
space cannot be factored, which is a characteristic of entan- 



JO C© ENTANGLEMENT 

glement. Nine years later, in 1935, Schrodinger actually 
named the phenomenon entanglement. He defined entangle- 
ment as follows: 

When two systems, of which we know the states by their respec- 
tive representation, enter into a temporary physical interaction 
due to known forces between them and when after a time of 
mutual influence the systems separate again, then they can no 
longer be described as before, viz., by endowing each of them 
with a representative of its own. I would not call that one but 
rather the characteristic trait of quantum mechanics. 9 

In 1927, Schrodinger was appointed to succeed Max Planck 
as a Professor at the University of Berlin, and in 1929 he was 
further elected to membership in the Prussian Academy of 
Sciences. Then in May 1933, he gave up his position in dis- 
gust after Hitler was elected Chancellor of Germany, and 
exiled himself to Oxford. In 1933, Schrodinger was awarded 
the Nobel Prize for his great achievements in physics. He 
shared the award with the English physicist Paul Dirac, who 
also made important contributions to the quantum theory 
and predicted the existence of antimatter based on purely 
theoretical considerations. 

Schrodinger returned to Austria and took up a professor- 
ship at the University of Graz. But when the Nazis took over 
Austria in 1938, he again escaped to Oxford. He did return 
to the Continent for one year and taught at Ghent, but as 
the War intensified he left for Dublin, where he became a 
professor of theoretical physics and held that position until 
1956. While living in exile in Ireland, in the spring of 1944, 



SHRODINGER AND HIS EQUATION Ca> yi 

Schrodinger became involved in another extramarital affair. 
He was then 57 years old, and he got entangled with a young 
married woman, Sheila May Greene. He wrote her poetry, 
watched her perform in plays, and fathered her baby girl. 
Anny offered to divorce him so he could marry Sheila, but 
Erwin refused. The affair ended and David, Sheila's husband, 
raised the girl despite the fact that he and Sheila later sepa- 
rated. In 1956, Erwin finally returned to Vienna. He died 
there in 1961, his wife, Anny, by his side. 



This Page Intentionally Left Blank 



8 

Heisenberg s Microscope 



"To get into the spirit of the quantum theory was, I would 
say, only possible in Copenhagen at that time." 

— Werner Heisenberg 



Werner Carl Heisenberg (1901-1976) was born 
outside Munich, in southern Germany, and when 
he was still a young child, his family moved into 
the city. Throughout his life, Heisenberg felt at home in 
Munich and returned to it again and again from wherever he 
was living. At his sixtieth birthday celebration, organized by 
the city, Heisenberg said: "Anyone who didn't experience 
Munich in the Twenties has no idea how splendid life can 
be." His father, August Heisenberg, was a professor of Greek 
philology at the University of Munich, and in fact was the 
only full professor of middle and modern Greek philosophy 
in Germany. The father imparted to Werner a love of Greek 
ideas, and Heisenberg never lost his love of Plato. (Ironically, 
the ancient Greek concepts of time and space and causality 
would come into conflict with new notions brought on by 



73 



J4 ® ENTANGLEMENT 

the quantum theory created by Heisenberg and his col- 
leagues.) While he was still in school, Heisenberg became 
interested in physics and decided to pursue a career as a sci- 
entist. He attended the University of Munich, and after fin- 
ishing his undergraduate studies remained to study for a 
Ph.D. in physics. 

In 1922, while a graduate student at Munich, Werner 
heard a public lecture on campus by Niels Bohr. He raised his 
hand and asked Bohr a hard question. When the lecture was 
over, Bohr came over to him and asked him to take a stroll. 
They walked for three hours, discussing physics. This was 
the beginning of a lifelong friendship. 

After finishing his studies, Heisenberg came to attend 
Bohr's insitute in Copenhagen and spent the years 1924- 
1927 there, learning both Danish and English while pursuing 
his other studies. By 1924, when he was 23, Heisenberg had 
already written twelve papers on quantum mechanics, several 
of them cowritten with the great physicists Max Born and 
Arnold Sommerfeld. Heisenberg became Bohr's favorite dis- 
ciple, and he often visited Bohr and his wife Margrethe at 
their home. When the big debate started between Einstein 
and Bohr, Heisenberg typically took Bohr's point of view, 
while Schrodinger sided with Einstein. This entanglement 
between Bohr and Heisenberg lasted throughout their lives. 

Heisenberg developed a theory of quantum mechanics 
equivalent to Schrodinger's. His version was finished a little 
before that of his senior colleague. While Schrodinger's 
approach used his wave equation, Heisenberg's solution was 
based on matrices, conceptually more challenging. Matrix 
mechanics uses numbers in rows and columns to predict the 



HEISENBERG'S MICROSCOPE CO) yj 

intensities of the light waves emitted from "excited" atoms 
changing energy levels as well as other quantum phenomena. 

It was later shown that the two methods are equivalent. In 
Heisenberg's more abstract approach, infinite matrices rep- 
resent properties of observable entities, and the mathematics 
used is the mathematics of matrix manipulations. Matrix 
multiplication is non-commutative, meaning that if we mul- 
tiply two matrices, A and B in the order AB, the answer, in 
general, will not be the same as the one we would get by per- 
forming the operation in reverse order, i.e., as BA. Contrast 
this with the way we multiply numbers, which is commuta- 
tive (for example, 5x7=35=7x5, so that the order of multi- 
plication does not matter and we get the same answer in both 
ways). The noncommutativity of the multiplication opera- 
tion on matrices has important consequences in quantum 
mechanics, which go beyond the work of Heisenberg. 

An observable (something about a quantum system that 
we may observe) is represented in modern quantum mechan- 
ics by the action of an operator on the wave function of the 
system. Some of these operators are commutative, meaning 
that if we apply one operator and then another to the system 
in the order AB, then the answer is the same as it would be 
if we applied the two operators in the reverse order: BA. 
Other operators are noncommutative, meaning that the order 
of applying the operators (and thus the order of making the 
observations) matters and the results are different from one 
another. For example, measuring the position of a particle is 
associated in quantum mechanics with applying the position 
operator to the wave function. Measuring the momentum of 
a particle is understood in quantum mechanics as applying 



j6 & ENTANGLEMENT 

the partial-derivative-with-respect-to-position operator to the 
wave function (momentum, p, is classically the mass of the 
particle times its velocity, and velocity is defined as the deriv- 
ative of position with respect to time). The two operators, 
position and momentum, do not commute with each other. 
That means that we cannot measure them both together, 
because if we measure one of them and then the other, our 
result would be different from what it would be if the order 
were reversed. The reason, in this example, for the noncom- 
mutativity of the two operators, position and momentum, 
can be seen by anyone who knows a little calculus: Deriva- 
tive (X^))^ +X(Derivative *P ), which does not equal 
X(Derivative \P ), which is an application of the two opera- 
tors in the reverse order. The reason for the first expression 
above is the rule for taking the derivative of a product. 

The fact that the two operators, X (position of the parti- 
cle) and Derivative (momentum of the particle) do not com- 
mute has immense consequences in quantum mechanics. It 
tells us that we cannot measure both the position and the 
momentum of the same particle and expect to get good accu- 
racy for both. If we know one of them to good precision (the 
one we measure first), then the other one will be known with 
poor precision. This fact is a mathematical consequence of 
the noncommutativity of the operators associated with these 
two kinds of measurements. This fact, that the position and 
the momentum of the same particle cannot both be localized 
with high precision is called the uncertainty principle, and it 
was also discovered by Werner Heisenberg. Heisenberg's 
uncertainty principle is his second important contribution to 
quantum theory after his formulation of matrix mechanics. 



HEISENBERG S MICROSCOPE © JJ 

Heisenberg's uncertainty principle is fundamental to quan- 
tum mechanics and brings into quantum mechanics the ideas 
of probability theory on a very basic level. It states that 
uncertainty cannot be removed from quantum systems. The 
uncertainty principle is stated as: 

ApAx>h 

Here Ap is the difference in, or uncertainty about, momen- 
tum. And Ax is the difference in, or uncertainty about, loca- 
tion. The principle says that the product of the uncertainty in 
the position of a particle and the uncertainty in the momen- 
tum of the particle is greater than or equal to Planck's con- 
stant. The implications of this seemingly-simple formula are 
immense. If we know the position of the particle to very high 
precision, then we cannot know its momentum better than 
some given level of accuracy, no matter how hard we try and 
no matter how good our instruments may be. Conversely, if 
we know the momentum of a particle to good accuracy, then 
we cannot know the position well. The uncertainty in the 
system can never go away or be diminished below the level 
prescribed by Heisenberg's formula. 

To demonstrate the uncertainty principle as applied to the 
position and momentum of a particle, we use Heisenberg's 
Microscope. In February of 1927, Bohr left Heisenberg to 
work alone in Copenhagen, and went skiing with his family 
in Norway. Being alone allowed Heisenberg's thoughts to 
wander freely, as he later described it, and he decided to make 
the uncertainty principle the central point of his interpreta- 
tion of the nascent quantum theory. He remembered a dis- 
cussion he'd had long before with a fellow student at 



y8 C© ENTANGLEMENT 

Gottingen, which gave him the idea of investigating the pos- 
sibility of determining the position of a particle with the aid 
of a gamma-ray microscope. This notion solidified in his 
mind the principle he had already derived without this anal- 
ogy. Heisenberg quickly wrote a letter to Wolfgang Pauli 
(another pioneer of the quantum theory) describing his 
thought-experiment about the use of a gamma-ray micro- 
scope to determine the position of a particle, and when he 
received Pauli's answer, he used the ideas in the letter to 
improve the paper he was writing. When Bohr returned from 
Norway, Heisenberg showed him the work, but Bohr was 
dissatisfied. Bohr wanted Heisenberg's argument to emanate 
from the duality between particles and waves. After a few 
weeks of arguments with Bohr, Heisenberg conceded that the 
uncertainty principle was tied-in with the other concepts of 
quantum mechanics, and the paper was ready for publica- 
tion. What is Heisenberg's microscope? The figure below 
shows the microscope. A ray of light is shone on a particle 
and is reflected into the lens. As the ray of light is reflected by 
the particle into the microscope, it exerts on the particle it 
illuminates some pressure, which deflects the particle from its 
expected trajectory. If we want to lower the effect of the 
impact on the particle, so as not to disturb its momentum 
much, we must increase the wavelength. But when the wave- 
length reaches a certain amount, the light entering the micro- 
scope misses the position of the particle. So, one way or the 
other, there is a minimum to the level of accuracy that is pos- 
sible to obtain for the product of position and momentum. 



heisenberg's microscope & 79 




Another important contribution by Heisenberg to quan- 
tum mechanics was his discussion of the concept of poten- 
tiality within quantum systems. What separates quantum 
mechanics from classical mechanics is that in the quantum 
world a potential is always present, in addition to what actu- 
ally happens. This is very important for the understanding of 



80 & ENTANGLEMENT 

entanglement. The phenomenon of entanglement is a quan- 
tum phenomenon, and has no classical analog. It is the exis- 
tence of potentialities that creates the entanglement. In 
particular, in a system of two entangled particles, the entan- 
glement is evident in the potential occurrence of both AB 
(particle 1 in state A and particle 2 in state B) and CD (par- 
ticle 1 in state C and particle 2 in state D). We will explore 
this further. 

The 1930s brought great changes to the life of Heisenberg 
and to science. In 1932, Heisenberg was awarded the Nobel 
Prize for his work in physics. The next year, Hitler came to 
power and German science began its collapse with Jewish aca- 
demics being fired by the Nazis. Heisenberg remained in Ger- 
many, watching his friends and colleagues leave for America 
and elsewhere. In an infamous SS paper, Heisenberg was 
reviled as a "white Jew," and "a Jew in spirit, inclination, and 
character," presumably for his apparent sympathy for his Jew- 
ish colleagues. But Heisenberg remained in Nazi Germany 
despite calls from his colleagues to leave. Just where his real 
sympathies were remains a mystery. There has been a sugges- 
tion that there were ties between Heisenberg's and Himmler's 
families. 10 It has been suggested that Heisenberg used that 
relationship to appeal directly to the leadership of the SS to 
end the diatribe against him. In 1937, the thirty-five year old 
Heisenberg, suffering from depression, met a twenty-two- 
year-old woman in a Leipzig bookshop. The two shared an 
interest in music, and performed together, he singing and she 
accompanying him on the piano. Within three months they 
were engaged, and shortly afterwards they were married. 



HEISENBERG S MICROSCOPE Ca> Hi 

In 1939, Heisenberg was called up for military service. By 
then he was the only leading physicist in Germany, and it 
was no surprise that for his military service the Nazis 
expected him to help them develop a nuclear bomb. In 1941, 
Heisenberg and his colleagues built a nuclear reactor, which 
they hid inside a cave under a church in a small village. For- 
tunately for humanity, Hitler's main project was Peenemu- 
nde, the Nazi effort to build missiles, which were directed at 
Britain, and the nuclear project was lower on the list of pri- 
orities. As it turned out, Heisenberg did not know how to 
make an atomic bomb, and the Manhattan Project in Amer- 
ica was far ahead of the Nazi effort. After the war, Heisen- 
berg remained a leading scientist in Germany, and he 
probably took with him to his grave the answers to the many 
questions humanity now has about the real role he played in 
the Nazi attempt to build a bomb. 



This Page Intentionally Left Blank 



9 

Wheeler's Cat 



"We will first understand how simple the universe is when 
we recognize how strange it is." 

— John Archibald Wheeler 



Many books on quantum mechanics tell the story 
Schrodinger used to illustrate a paradox based on 
the superposition of states. This story has come to 
be known as "Schrodinger's Cat." Schrodinger imagined a 
cat placed in a closed box along with an apparatus contain- 
ing a speck of radioactive material. Part of the apparatus is 
a detector that controls a mechanism to break an attached 
vial of cyanide. When an atom of the radioactive element 
undergoes a disintegration that is registered by the detector, 
the vial is broken, killing the cat. Because the radioactive dis- 
integration is a quantum event, the two states — the cat alive, 
and the cat dead — can be superimposed. Thus, before we 
open the box and make a measurement — i.e., before we actu- 
ally find out whether the cat is dead or alive — the cat is both 
dead and alive at the same time. Besides the unpleasant impli- 



83 



84 & ENTANGLEMENT 

cations, this example is not terribly instructive. Murray Gell- 
Mann says in his book The Quark and the Jaguar that 
Schrodinger's Cat is no better an example than that of open- 
ing the box containing a cat that has spent a long flight in the 
baggage hold of a plane. The owner of the arriving cat 
inevitably asks the terrifying question upon receiving the con- 
tainer at the baggage claim: Is my cat dead or alive? Accord- 
ing to Gell-Mann the problem with the Schrodinger Cat 
example is that of decoherence. A cat is a large, macroscopic 
system, not an element of the microscopic quantum world. 
As such, the cat interacts with its environment very exten- 
sively: it breathes air, it absorbs and emits heat radiation, it 
eats and drinks. Therefore, it is impossible for the cat to 
behave in the very specific quantum way, in which it hangs on 
the balance "both dead and alive," as an electron in a super- 
position of more than one state. 

I still like using a cat to make this point, but we don't have 
to have it dead, so our example will not be macabre. We will 
think of a cat being at two places at once, just as the electron. 
Think of an electron as a cat, Wheeler's Cat. 

John Archibald Wheeler had a cat that lived with him and 
his family in Princeton. Einstein's house was only a short dis- 
tance away, and the cat seemed to like Einstein's house. 
Wheeler would often see Einstein walking home, flanked by 
his two assistants, and sure enough, within a few minutes 
the phone would ring and Einstein would be on the line ask- 
ing him whether he wanted him to bring back his cat. Imag- 
ine a cat that — instead of being dead and alive at the same 
time as in Schrodinger's example — is in the superposition of 
being both at Einstein's house and at Wheeler's house. When 



wheeler's cat & 8j 

we take a measurement: Einstein or Wheeler looking for the 
cat, the cat is forced onto one of the two states, just as a par- 
ticle or a photon. 

The idea of a superposition of states is important in quan- 
tum mechanics. A particle can be in two states at the same 
time. Wheeler's cat, let us assume, can be in a superposition 
of the two states. The cat can be both at Wheeler's house 
and at Einstein's house. As Michael Home likes to point out, 
in quantum mechanics we abandon the quotidian "either- 
or" logic in favor of the new "both-and" logic. And indeed, 
the concept is very foreign since we never encounter it in our 
daily lives. There are, perhaps, still some examples that can 
be made. I'm at the bank, and there are two lines in front of 
the teller windows. They're both equally long, and there's 
no one behind me. I want to be in the line that moves the 
fastest, but I don't know which one that will be. I stand 
between the two lines, or I keep jumping from one line to 
the other as one and the other becomes shorter. I am in "both 
lines at once." I am in a superposition of the two states: (I'm 
in line 1) and ( I'm in line 2). Returning to Wheeler's cat, the 
cat is in a superposition of the following two states: 

(Cat at Wheeler's house) and (Cat at Einstein's house). Of 
course, in the original Schrodinger's Cat story, the cat is in a 
sadder superposition: (Cat is dead) and (Cat is alive). 

John Archibald Wheeler was born in Jacksonville, Florida, in 
1911. He received his doctorate in physics from Johns Hop- 
kins University in 1933, and he also studied physics with 
Niels Bohr in Copenhagen. He took a professorship of 
physics at Princeton University, and his star student there 



86 & ENTANGLEMENT 

was Richard Feynman (1918-1988). Feynman, who years 
later won a Nobel Prize and became one of the most famous 
American physicists, wrote his brilliant dissertation under 
Wheeler, leading to his doctorate from Princeton in 1942. 
The thesis, growing out of earlier work by Paul A. M. Dirac, 
introduced an important idea into quantum mechanics. It 
was an application of the classical principle of least action to 
the quantum world. What Feynman did was to create the 
sum-over-histories approach to quantum mechanics. This 
approach considers all possible paths a particle (or system) 
may take in going from one point to another. Each path has 
its own probability, and it is therefore possible to discover the 
most probable path the particle has taken. In Feynman's for- 
mulation, the wave-amplitudes attached to all possible paths 
are used to derive a total amplitude, and hence a probability 
distribution, for the outcomes at the common terminus of all 
possible paths. 

Wheeler was very excited about Feynman's work, and 
took the manuscript of Feynman's thesis to Einstein. "Isn't 
this wonderful?" he asked. "Doesn't this make you believe in 
the quantum theory?" Einstein read the thesis, thought about 
it for a moment, and then said: "I still don't believe that God 
plays dice . . . but maybe I've earned the right to make my 
mistakes." 11 

Paul A.M. Dirac (1902-1984) was a British physicist who 
started his career as an electrical engineer. Since he had diffi- 
culties finding employment in his field, he applied for a fel- 
lowship at Cambridge University. Eventually he became one 
of the key figures in physics in the twentieth century and won 



wheeler's cat & 87 

the Nobel Prize. Dirac developed a theory that combined 
quantum mechanics with special relativity. His work thus 
allowed the equations of quantum mechanics to be corrected 
for relativistic effects for particles moving at close to the speed 
of light. As part of his research, Dirac predicted the existence 
of anti-particles. Dirac's paper on the theoretical possibility 
that anti-particles may exist was published in 1930, and a 
year later the American physicist Carl Anderson discovered 
the positron, the positively charged anti-electron, while ana- 
lyzing cosmic rays. The electron and the positron annihilate 
each other when they meet, producing two photons. 

In 1946, Wheeler proposed that the pair of photons pro- 
duced when a positron and an electron annihilate each other 
could be used to test the theory of quantum electrodynamics. 
According to this theory, the two photons should have oppo- 
site polarizations: if one is vertically polarized, then the other 
one must be polarized horizontally. "Polarization" means the 
direction in space of either the electric or the magnetic fields 
of light. 

In 1949, Chien-Shiung Wu (known as "Madame Wu," 
echoing the way physicists referred to Marie Curie) and Irv- 
ing Shaknov, of Columbia University, carried out the exper- 
iment that Wheeler had suggested. Wu and Shaknov 
produced positronium, an artificial element made of an elec- 
tron and a positron circling each other. This element lives for 
a fraction of a second, and then the electron and positron 
spiral toward each other, causing mutual annihilation that 
releases two photons. Wu and Shaknov used anthracene crys- 
tals to analyze the polarization direction of the resulting pho- 
tons. Their result confirmed Wheeler's prediction: the two 



ENTANGLEMENT 



photons were of opposite polarization. The 1949 Wu and 
Shaknov experiment was the first one in history to produce 
entangled photons, although this important fact was only 
recognized eight years later, in 1957, by Bohm and 
Aharonov. 

Wheeler made important contributions to many areas of 
physics in addition to quantum mechanics. These include the 
theories of gravitation, relativity, and cosmology. He invented 
the term black hole to describe the spacetime singularity that 
results when a massive star dies. Together with Niels Bohr, 
Wheeler discovered fission. In January 2001, at age 90, 
Wheeler suffered a heart attack. The illness changed his view 
of life, and he decided that he wanted to spend his remain- 
ing time working on the most important problems in physics: 
the problems of the quantum. 

According to Wheeler, the problem of the quantum is the 
problem of being, of existence. He vividly recalls the story, 
related by H. Casimir, a fellow student of Bohr, of the debate 
on the quantum between Bohr and Heisenberg. The two 
were invited by the philosopher Hoffding, a mutual friend, to 
his home to discuss the Young double-slit experiment and its 
implications about the quantum. Where did the particle go? 
Did it pass through one slit or the other? As the discussion 
progressed, Bohr mulled the issue and muttered: "To be . . . 
to be . . . what does it mean to be?" 

John Wheeler himself later took the Young double-slit 
experiment to a new level. He showed in a cogent and elegant 
way that within a variant of this experiment, with the mere 
act of measurement, an experimenter can change history. By 



WHEELER S CAT & 89 

deciding whether we want to measure something one way, or 
another, the experimenter, a human being, can determine 
what "shall have happened in the past." The following 
description of Wheeler's experimental setup is adapted from 
his paper, "Law without Law." 12 

Wheeler described in the article a modern variant of 
Young's double-slit experimental setup. The figure below 
shows the usual double-slit arrangement. 



Source 



n 



Wall 



I 

Backstop 




Light rays hit the screen with the slits and produce two 
sets of waves, as would happen with water waves as they 
leave the two slits. Where they meet, the light waves interact 
with each other. They interfere constructively to result in a 
higher amplitude wave, and destructively, canceling each 
other or producing waves of lower amplitude. The modern 
setup uses mirrors instead of slits, and it uses laser light, 
which can be controlled much more precisely than regular 
light. In more advanced experimental arrangements, fiber 
optics are used as the medium of choice for experiments. 

The simplest of the setups for the analog of the double-slit 



5>0 C© ENTANGLEMENT 

experiment is shown below. We have a diamond design, in 
which light from a source is aimed at a half-silvered mirror 
that allows half the light to go through and half to be 
reflected. Such a mirror is called a beam splitter since it splits 
an arriving light beam into two beams: the reflected beam 
and the transmitted beam. The beams are then each reflected 
by a mirror and are allowed to cross and then be detected. By 
noting which detector clicks to register the arrival of a pho- 
ton, the experimenter is able to tell by which route the pho- 
ton has traveled: Was the photon transmitted by the beam 
splitter, or was it reflected through it? Alternatively, the 
experimenter can place another beam splitter (half-silvered 
mirror) right at the point of crossing of the two beams. Such 
a placement of the mirror will cause the beams to interfere 
with each other, just as in the double-slit experiment. Here, 
only one detector will click (where the beams interfere con- 
structively) and the other will not (since there the beams 
interfere destructively). When this happens in an experiment 
with very weak light that sends only one photon at a time, we 
find that the photon travels both paths — it is both reflected 
and transmitted at the first beam splitter (or else there would 
be no interference: both detectors would click, which does 
not happen). 

Wheeler says that Einstein, who used a similar idea in a 
thought experiment, argued that "it is unreasonable for a 
single photon to travel simultaneously two routes. Remove 
the half-silvered mirror, and one finds that one counter goes 
off, or the other. Thus the photon has traveled only one 
route. It travels only one route, but it travels both routes; it 
travels both routes, but it travels only one route. What non- 
sense! How obvious it is that quantum theory is inconsis- 



WHEELER S CAT & 5>J 



tent! Bohr emphasized that there is no inconsistency. We are 
dealing with two different experiments. The one with the 
half-silvered mirror removed tells which route. The one with 
the half-silvered mirror in place provides evidence that the 
photon traveled both routes. But it is impossible to do both 
experiments at once." 13 

Wheeler asked the question: Can the experimenter deter- 
mine by which route the photon travels? If the experimenter 
leaves out the second beam splitter, then the detectors indi- 
cate by which route the photon traveled. If the second beam 
splitter is in place, we know from the fact that one detector 
clicks and not the other that the photon has traveled both 
paths. Before the decision is made whether to insert the beam 
splitter, one can only describe the photon in the interferom- 
eter as being in a state with several potentialities (since poten- 
tialities can coexist). The choice of inserting or not inserting 
the beam splitter determines which potentiality is actualized. 
The two setups are shown below. 




^ -.DELAYED" 
, CHOICE: 
^S IN OR OUT-* 




BOTH 
ROUTES? 




5>2 C© ENTANGLEMENT 

The amazing thing, according to Wheeler, is that by 
delayed choice, the experimenter can change history. The 
experimenter can determine whether or not to place the sec- 
ond beam splitter after the photon has traveled most of the 
way to its destination. Modern science allows us to randomly 
choose the action (place the beam splitter or not place it) so 
quickly — within a very, very small fraction of a second — so 
that the photon will have already done its travel. When we 
do so, we are determining, after the fact, which route the 
photon shall have traveled. Shall it have traveled one route, 
or shall it have traveled both routes? 

Wheeler then took his outlandish idea to the cosmic 
scale. 14 He asked: "How did the universe come into being? Is 
that some strange, far-off process, beyond hope of analysis? 
Or is the mechanism that came into play one which all the 
time shows itself?" Wheeler thus tied the big bang and the 
creation of the universe to a quantum event, and he did so 
years before the cosmologists of the 1980s and 1990s came 
up with the idea that the galaxies were formed because of 
quantum fluctuations in the primordial soup of the big bang. 
Wheeler's answer to creation, history, and the birth of the 
universe is that we should look at the delayed-choice exper- 
iment. Such an experiment "reaches back into the past in 
apparent opposition to the normal order of time." He gives 
the example of a quasar, known as 0957+56iA,B, which sci- 
entists had once thought to be two objects but now believe 
is one quasar. The light from this quasar is split around an 
intervening galaxy between us and the quasar. This inter- 
vening galaxy acts as a "gravitational lens," about which the 
light of the quasar is split. The galaxy takes two light rays, 



wheeler's cat & 93 

spread apart by fifty thousand light years on their way from 
the quasar to Earth, and brings them back together on Earth. 
We can perform a delayed-choice split-beam experiment with 
the quasar acting as the half-silvered mirror and the inter- 
vening galaxy as the two full mirrors in the experimental 
setup used in the laboratory. Thus we have a quantum exper- 
iment on a cosmic scale. Instead of a few meters' distance, as 
in the lab, here we have an experiment with distances of bil- 
lions of light years. But the principle is the same. 

Wheeler says: "We get up in the morning and spend the day 
in meditation whether to observe by 'which route' or to 
observe interference between 'both routes.' When night comes 
and the telescope is at last usable, we leave the half-silvered 
mirror out or put it in, according to our choice. The mono- 
chromatizing filter placed over the telescope makes the count- 
ing rate low. We may have to wait an hour for the first photon. 
When it triggers a counter, we discover 'by which route' it 
came with the one arrangement; or by the other, what the rel- 
ative phase is of the waves associated with the passage of the 
photon from source to receptor 'by both routes' — perhaps 
50,000 light years apart as they pass the lensing galaxy g-i. But 
the photon has already passed that galaxy billions of years 
before we made our decision. This is the sense in which, in a 
loose way of speaking, we decide what the photon shall have 
done after it has already done it. In actuality it is wrong to talk 
of the 'route' of the photon. For a proper way of speaking we 
recall once more that it makes no sense to talk of the phe- 
nomenon until it has been brought to a close by an irreversible 
act of amplification: 'No elementary phenomenon is a phe- 
nomenon until it is a registered (observed) phenomenon.'" 



94 <3> ENTANGLEMENT 





Reproduced from J. A. Wheeler, Law without Law, 
Wheeler and Zureck, eds., 1983. 



io 

The Hungarian Mathematician 



"I do know, though, that when in Princeton Bohr would 
often discuss measurement theory with Johnny von Neu- 
mann who pioneered the field. As I see it, these considera- 
tions have led to contributions, important ones, to 
mathematics rather than to physics." 

— Abraham Pais 



TTancsi ("Johnny") Neumann was born in Budapest on 

m December 28, 1903, to a wealthy family of bankers. 

m Between 1870 and 1910, Budapest saw an unprece- 
dented economic boom, and many talented people migrated 
there from the Hungarian countryside and from other nations 
to pursue the opportunities that this thriving European capi- 
tal had to offer. By 1900 Budapest boasted 600 coffeehouses, 
numerous playhouses, a renowned symphony and opera com- 
pany, and an educational system that was the envy of Europe. 
Ambitious, hard-working people thronged to Budapest, where 
they had a chance of achieving success in the growing eco- 
nomic life of the city. Among the newcomers were many Jews 
who flocked from all over Europe to a city known for its reli- 
gious tolerance and enlightened population. 15 

Johnny's parents, Max and Margaret Neumann, came to 



95 



5>6 C© ENTANGLEMENT 

Budapest from the town of Pecs, on the Yugoslav border, as 
many Jews did during that time, the late 1800s. Max worked 
hard but was handsomely rewarded and within a few years 
became a powerful executive at a successful Hungarian bank 
that prospered from lending money to small business owners 
as well as agricultural corporations. Max did so well, in fact, 
that within a few years he was able to buy his family an 18- 
room apartment in a building in which several other wealthy 
Jewish families resided. One of them was the family of his 
brother-in-law. The children of the two families roamed the 
floors of the building together, running in and out of both 
palatial apartments. 

In addition to financial success, Max Neumann achieved a 
degree of influence over Hungarian politics. As a major fig- 
ure in Hungarian society and a successful financial advisor to 
the Hungarian Government, Max Neumann was rewarded 
with a hereditary nobility title in 1913. This was the Hun- 
garian equivalent of being knighted by the Queen of England. 
In addition to the great honor — rare for Jews — Max could 
now add the prefix von to his name. He became Max von 
Neumann, a member of the Hungarian nobility. His sons, 
John, the firstborn, and his two brothers, Michael and 
Nicholas, enjoyed the same privilege. At age 10, the young 
Jancsi Neumann thus became John von Neumann, and 
throughout his life he cherished his noble European status. 
The family even drew its own coat of arms, including a rab- 
bit, a cat, and a rooster. Max thought that Johnny was like 
a rooster because he sometimes used to crow; Michael looked 
like a cat; and Nicholas, the youngest, was the rabbit. The 
von Neumanns exhibited their coat of arms at their impres- 



THE HUNGARIAN MATHEMATICIAN <B 97 

sive apartment in the city and also on the gate of the sump- 
tuous country estate they later bought, where they spent their 
summers. The family not only became members of the Hun- 
garian aristocracy, they ranked among its staunchest defend- 
ers. After Bela Kun established Communist rule in 1919, 
Max von Neumann went to Vienna and summoned Admiral 
Horthy to attack Kun's forces and retake Hungary, freeing it 
from Communism for the first time (this happened a second 
time after the collapse of the Soviet Union). 

In the fateful year 1913, when the family received its nobil- 
ity and war was declared across Europe, Johnny began to 
exhibit the startling intellectual capacity that in time separated 
him from the rest of his family, and everyone else around him. 
The discovery was made, innocently enough, when his father 
asked the ten-year-old to multiply two numbers and the boy 
completed the task with amazing speed. Max then gave Johnny 
two huge numbers to multiply, and the child completed the 
calculation in seconds. This stunned the father and he began 
to realize that this was no ordinary child. Johnny was gifted far 
beyond what anyone had imagined. 

Only later came the revelations that at school Johnny knew 
more about the material he was taught than did his teachers. 
In conversations around the family dinner table he was far 
ahead of all the other family members in his understanding 
of the issues and ideas discussed. 

When his parents understood that their firstborn child was 
so prodigiously gifted, they did not waste the opportunity to 
prepare him for greatness. They hired private tutors to teach 
him advanced mathematics and science. And the father led 
intellectual discussions around the dinner table in which 



98 C© ENTANGLEMENT 

every family member was expected to contribute to the dis- 
cussion. This allowed the young genius to further refine his 
skills. 

At age eleven, Johnny was sent to the gymnasium, the 
European institution similar to a high school, which nor- 
mally accepted students several years older. At the gymna- 
sium Johnny studied mathematics, Greek, Latin, and other 
subjects. He excelled in all of them. Laslo Ratz, an instruc- 
tor of mathematics at the gymnasium, quickly realized that 
he had a genius in his class. He went to Max von Neumann 
and suggested that the family provide their son with even 
more training in mathematics. It was arranged that Ratz 
would take Johnny out of the regular math class three times 
a week and teach him privately. But soon Ratz realized that 
Johnny knew more than he did. Ratz took Johnny to the Uni- 
versity of Budapest. Here the boy — clearly the youngest per- 
son ever to attend the university — enrolled in classes in 
advanced mathematics. 

A year after he started taking classes at the university, a 
fellow student (years older) asked Johnny if he had heard of 
a particular theorem in number theory. Johnny knew the the- 
orem — it was an unproven result that many mathematicians 
had worked on. His friend (who years later won a Nobel 
Prize) asked him if he could prove it. Johnny worked on the 
theorem for several hours, and proved it. Within a year he 
enrolled at the renowned technical university in Zurich, the 
ETH (Einstein's alma mater), and a short time later at the 
University of Berlin. At all three institutions he stunned 
renowned mathematicians, among them the famous David 
Hilbert (1862-1943), with his keen understanding of math- 



THE HUNGARIAN MATHEMATICIAN & 99 

ematics and his incredible ability to compute and analyze 
problems with unparalleled speed. 

When solving a mathematical problem, von Neumann 
would face a wall, his face would lose all expression, and he 
would mutter to himself for several minutes. Completely 
immersed in the problem, he would not hear or see anything 
that was happening around him. Then suddenly his face 
would assume its normal expression, he would turn back 
from the wall, and quietly state the answer to the problem. 

Johnny von Neumann was not the only outstanding intel- 
lect that Budapest produced during those years. Six Nobel 
Prize winners were born in Budapest between 1875 an d 1 9°5 
(five of them Jewish). Four other leaders of modern science 
and mathematics were also born in Budapest during this 
period. All of them had attended the superb schools of Hun- 
gary, the gymnasia, and were nurtured at home. Half a cen- 
tury later, Nobel laureate Eugene Wigner, who was one of 
these ten geniuses, was asked what he thought was the rea- 
son for the phenomenon. Wigner replied that he didn't 
understand the question. "Hungary has produced only one 
genius," he said. "His name is John von Neumann." 

Most of the Hungarian prodigies emigrated to the United 
States, where their influence on the development of modern 
science was immense. When they arrived in America, their 
special gifts stunned the scientific community, and some 
began to half-seriously speculate that the foreign scientists 
were not Hungarian, but aliens from outer space bent on 
dominating American science. Theodore von Karman was 
the first of the ten to come to America. He was followed by 
Edward Teller and the others, including John von Neumann, 



100 C® ENTANGLEMENT 



in the 1930s. When Teller arrived, he was confronted with 
the story about the extraterrestrial origin of these geniuses. 
Teller assumed a worried expression. Then he said: "von Kar- 
man must have been talking." 

But before immigrating to the United States, Johnny von 
Neumann — arguably the greatest genius of them all — 
received further superb training in mathematics and science 
that helped transform him into one of the greatest mathe- 
maticians of his age. This training took place at the univer- 
sities of Zurich, Gottingen, and Berlin. 

In 1926, von Neumann came to Gottingen and heard a 
lecture by Werner Heisenberg on matrix mechanics and the 
difference between his approach to quantum mechanics and 
that of Schrodinger (roughly the same talk the author heard 
in Berkeley 46 years later). In the audience was also David 
Hilbert, the greatest mathematician of the time. According to 
Norman Macrae (John von Neumann, AMS, 1999), Hilbert 
didn't understand the quantum theory as presented by 
Heisenberg and asked his assistant to explain it. Von Neu- 
mann saw this and decided to explain quantum theory to the 
old mathematician in terms that he could understand, that is, 
in mathematical language. In doing so, von Neumann used 
the ideas of Hilbert Space, much to the delight of Hilbert. 

To this day, physicists use Hilbert space to explain and ana- 
lyze the world of the very small. A Hilbert space is a linear 
vector space with a norm (a measure of distance) and the 
property of completeness. 

Von Neumann expanded the paper he wrote for Hilbert 
in 1926 into a book called The Mathematical Foundations of 
Quantum Mechanics, published in 1932. Von Neumann 



THE HUNGARIAN MATHEMATICIAN & 101 

demonstrated that the geometry of vectors over the complex 
plane has the same formal properties of the states of a quan- 
tum mechanical system. He also derived a theorem, using 
some assumptions about the physical world, which proved 
that there are no "hidden variables," whose inclusion could 
reduce the uncertainty in quantum systems. While posterity 
would agree with his conclusion, John Bell successfully chal- 
lenged von Neumann's assumptions in his daring papers of 
the 1960s. Still, von Neumann was one of the founders of the 
mathematical foundations of the quantum theory, and his 
work is important in establishing mathematical models for 
the inexplicable physical phenomena of the quantum world. 
Key among these concepts is the idea of a Hilbert space. 

A Hilbert space, denoted by H, is a complete linear vector 
space (where complete means that sequences of elements in 
this space converge to elements of the space). As applied in 
physics, the space is defined over the complex numbers, 
which is needed in order to endow the space with the neces- 
sary richness for making it the proper model in different sit- 
uations. Complex numbers are numbers that may contain 
the element z, the square root of negative one. The Hilbert 
space H allows the physicist to manipulate vectors, that is, 
mathematical entities that have both a magnitude and a 
direction: little arrows in Hilbert space. These arrows can be 
added to or subtracted from each other, as well as multiplied 
by numbers. These arrows are the mathematical essentials of 
the physical theory since they represent states of quantum 
systems. 

Von Neumann came to the Institute for Advanced Studies 
at Princeton in the early 1930s. He and Einstein never saw 



102 & ENTANGLEMENT 



eye to eye. Their differences were mostly political — von Neu- 
mann found Einstein naive, believing, himself, that all left- 
leaning governments were weak, and dogmatically 
supporting conservative policies. He was involved with the 
Manhattan Project and, unlike most other scientists who con- 
tributed to the making of the bomb, never appeared to have 
battled any moral dilemmas as a result of this work. 

No one questions the fact that von Neumann made great 
contributions to the quantum theory. His book on the sub- 
ject has become an indispensable tool for practitioners and an 
important treatise on the mathematical foundations of quan- 
tum mechanics. 

Eugene Wigner, who later won the Nobel Prize for his 
work in physics, came to Princeton after John von Neumann 
was already established there. Some have said that Wigner 
was hired by Princeton from Hungary so that "Johnny" 
wouldn't be lonely and would have someone who could 
speak Hungarian with him. When von Neumann's seminal 
book appeared in English, Wigner told Abner Shimony: "I 
have learned much about quantum theory from Johnny, but 
the material in his Chapter Six [on measurement] Johnny 
learned all from me." Von Neumann's book contained an 
argument that was important in subsequent discussions of 
the interpretations of quantum mechanics, namely a proof 
that the quantum theory could not be "completed" by a hid- 
den-variables theory in which every observable has a definite 
value. His proof of this proposition was mathematically cor- 
rect, but was based on a premise that is dubious from a phys- 
ical point of view. This flaw in von Neumann's book was 
exposed decades later by John Bell. 



11 

Enter Einstein 



"The elementary processes make the establishment of a 
truly quantum-based theory of radiation appear almost 
inevitable." 

— Albert Einstein 



^lbert Einstein was born in Ulm, in southern Germany, 
/ 1 in 1879 to a middle-class Jewish family. His father 
JL JL and uncle owned an electrochemical business, 
which kept failing. As a result, the family moved to Munich, 
then to a couple of places in northern Italy, and finally back 
to Germany. Einstein was educated in Switzerland, and his 
first job was famously that of technical expert at the Swiss 
Patent Office in Bern. There, in the year 1905, Einstein pub- 
lished three papers that changed the world. These papers 
were his expositions of the three theories he developed while 
working alone at the patent office: the special theory of rel- 
ativity; a theory of Brownian motion and a new formulation 
of statistical thermodynamics; and a theory of the photo- 
electric effect. 

Einstein's life and his development of the theories of rela- 



103 



104 c ® ENTANGLEMENT 

tivity have been discussed in detail. 16 But Einstein exerted a 
very important influence on the quantum theory from its 
inception. Soon after he read Planck's paper about the quan- 
tum in 1900, Einstein began to ponder the nature of light in 
view of the new theory. He proposed the hypothesis that light 
is a stream of particles, or quanta. 

Einstein studied the effect of the interaction of light with 
matter. When light rays strike a metal, electrons are emitted. 
These electrons can be detected and their energies measured. 
This was proved using a number of experiments by the 
American physicist Robert Millikan (1868-1953). The analy- 
sis of the photoelectric effect in various metals and using light 
of different frequencies revealed the following phenomena: 
When light of low frequency, up to a threshold frequency Vq, 
shines on a metallic surface, no photoelectrons are emitted. 
For a frequency above the threshold, photoelectrons are emit- 
ted and as the intensity of the light of this frequency is var- 
ied, the number of photoelectrons varies but their energy 
remains the same. The energy of the photoelectrons increases 
only if the frequency is increased. The threshold frequency, 
Vq, depends on the kind of metal used. 

The classical theory of light does not explain the above phe- 
nomena. Why shouldn't the intensity of light increase the 
energy of the photoelectrons? And why would the frequency 
affect the energy of these electrons? Why are no photoelectrons 
released when the frequency is below some given level? What 
Einstein did in his research culminating with the paper of 1905 
was to assume that light consisted of particles — later called pho- 
tons — and to apply Planck's quantum idea to these photons. 

Einstein viewed the photons as discrete little packages of 



ENTER EINSTEIN & IOJ 

energy flying through space. Their energy was determined by 
Einstein's formula: E=hv. (Where h is Planck's constant and 
V is the frequency of the light.) 

The connection between this formula and Planck's earlier 
equation is simple. Recall that Planck had said that the only 
possible energy levels for a light-emitting system (i.e., an 
oscillating charge) are: 

£=0, h V, 2h V, 3h V Ah V . . . , or in general, nh V, where n is a 
positive integer. 

Clearly, the smallest amount of energy that can be emitted by 
the system is the difference between two adjacent Planck val- 
ues, which is: ^v, hence Einstein's formula for the energy of 
the smallest possible amount of light. 

We see from Einstein's formula that the intensity of the 
light does not increase the energy of its photons, but only 
increases the number of photons emitted, the energy of each 
photon being determined by the frequency of the light (mul- 
tiplied by Planck's constant). In order to disengage an elec- 
tron from the lattice of atoms in the metal, some minimum 
energy is required, denoted by W (which stands for 
"work" — the work necessary to dislodge one electron). Thus 
when the frequency reaches some minimum level, the energy 
imparted to the electron passes the threshold W, and the elec- 
tron is released. Einstein's law for explaining the photoelec- 
tric effect is given by the formula: 

K=hv-W 

Where K is the kinetic energy of the released electron. This 
energy is equal to Einstein's energy (E=hv) minus the mini- 



106 C® ENTANGLEMENT 

mum level needed to dislodge the electron, W. The formula 
explained the photoelectric effect perfectly. This elegant 
theory of the interaction of light with matter, a quantum 
theory of a known and previously-misunderstood effect, won 
Einstein the Nobel Prize in 1921. He was notified of the Prize 
while on a visit to Japan. Curiously, Einstein never received 
a Nobel Prize for his special theory of relativity, nor for his 
general theory of relativity, two theories that revolutionized 
modern science. 

So Einstein was there when the quantum theory was born, 
and was one of the "fathers" of the new theory. He felt he 
understood nature very well, as evidenced by the fact that he 
could propose such revolutionary theories — his special 
theory of relativity of 1905 and the general theory of rela- 
tivity of 1916 — that explained ever more phenomena in the 
realm of the large and fast. But even though he was an 
incomparable master of the physics of the macro-world, and 
contributed much to the quantum theory of the very small, 
Einstein's philosophy clashed with the advancing interpreta- 
tion of quantum mechanics. Einstein could not give up his 
belief that God does not play dice, meaning that chance has 
no place within the laws of nature. He believed that quantum 
mechanics was correct to attribute probabilities to possible 
outcomes of an experiment, but he thought that the need to 
resort to probabilities was due to our ignorance of a deeper 
level of the theory, which is describable by deterministic (i.e., 
devoid of a probability-structure) physics. That is the mean- 
ing of his oft-quoted statement about God and dice. 

Quantum theory was — and still is — based on probabilities 
rather than exact predictions. As the Heisenberg uncertainty 



ENTER EINSTEIN <© IOJ 

principle specifies, it is impossible to know both the momen- 
tum of a particle and its location — if one is known with some 
precision, the other, of necessity, can only be known with 
uncertainty. But the randomness, the variation, the fuzziness, 
the uncertainty in the new physical theory goes beyond its 
manifestation in the uncertainty principle. Recall that parti- 
cles and photons are both wave and particle and that each 
has its wave function. What is this "wave function"? It is 
something that leads directly to probabilities, since the square 
of the amplitude of the wave we associate with any particle 
/s, in fact, a probability distribution (the rule that assigns 
probabilities of various outcomes) for a particle's position. 
To obtain the probability distribution of the outcome of a 
measurement of other observable quantities (such as momen- 
tum), the physicist must perform a calculation that uses both 
the wave function and the operator representing the observ- 
able quantity of interest. 

Quantum theory is probabilistic on a very basic, very fun- 
damental level. There is no escape from the probabilities 
regardless of what we do. There is a minimum level of uncer- 
tainty about outcomes, which can never be diminished, 
according to the theory, no matter how hard we try. The 
quantum theory is thus very different from other theories 
that use probabilities. In economics, for example, there is no 
theory that states unequivocally that we cannot know some 
variable to a level of precision we desire. Here, the proba- 
bilities represent our lack of knowledge, not a fundamental 
property of nature. Einstein was a great critic of the quantum 
theory because he did not like to think that nature works 
probabilistically. God decrees, He does not play dice. Thus, 



108 C© ENTANGLEMENT 

Einstein believed that there was something missing from the 
quantum theory, some variables, perhaps, such that if we 
could find the values of these variables, the uncertainty — the 
randomness, the "dice" — would be gone. With the augmen- 
tation of these variables, the theory would be complete and 
would thus be like Newton's theory, in which variables and 
quantities may be known and predicted with great precision. 

In addition to his dislike for randomness and probability 
within a theory of nature, Einstein had other notions — ones 
that were "intuitive" to him, and would be so to most 
people. These were notions of realism and of locality. To Ein- 
stein, a facet of reality is something real, which a good theory 
of nature should include. If something happens somewhere, 
and we can predict it will happen without disturbing the sys- 
tem, then what happens is an element of reality. If a particle 
is located at a given spot, and we can predict that it will be 
there without disturbing it, then that is an element of reality. 
If a particle spins in a certain direction, and we can predict 
that it will spin in this direction without disturbing it, then 
this is an element of reality. Locality is the intuitive notion 
that something that happens in one place should not affect 
whatever happens at a far away location, unless, of course, 
a signal is sent to the other location (at the speed of light or 
less, as dictated by the special theory of relativity) and can 
make a difference there. 

Throughout his life, Einstein held fast to these three prin- 
ciples he believed should be part of a good description of 
nature: 



ENTER EINSTEIN Co JOp 

i. The fundamental level of nature should be 
described in principle by a deterministic theory, even 
though gaps in human knowledge about initial and 
boundary conditions may force human beings to resort 
to probability in making predictions about the outcomes 
of observations. 

2. The theory should include all elements of reality. 

3. The theory should be local: what happens here 
depends on elements of reality located here, and what- 
ever happens there depends on elements of reality 
located there. 

Einstein and his collaborators found that these notions, 
which seemed very natural to them, implied the incomplete- 
ness of the quantum theory — a theory that Einstein himself 
had helped bring about. As we will see, the above principles 
were eventually shown to be incompatible with quantum 
theory, but this would only happen in the 1960s. And mount- 
ing experimental evidence collected since the 1970s would 
further imply that quantum theory was correct. 

In the spring of 1910, the Belgian industrialist Ernest Solvay 
came up with the idea of organizing a scientific conference. 
The route to this idea was somewhat circuitous and bizarre. 
Solvay had developed a method for manufacturing soda and 
as a result became very wealthy. This gave him a high level 
of confidence in his own abilities, and, since he was inter- 
ested in science, he began to dabble in physics. Solvay 
invented a theory of gravitation and matter, which had little 
to do with reality or with science. But since he was so 



110 & ENTANGLEMENT 

wealthy, people listened to him, even if they could tell that his 
theories were nonsensical. The German scientist Walther 
Nernst told Solvay that he could get an audience for his 
theories if he would organize a conference for the greatest 
physicists of the day, and present to them his theories. Solvay 
fell for the idea, and thus the Solvay Conferences were born. 

The first Conseil Solvay took place at the Metropole Hotel 
in Brussels in late October 1911. Invitations were sent to the 
best-known physicists, including Einstein, Planck, Madame 
Curie, Lorentz, and others, and all the invitees accepted and 
attended what became a historic meeting. The conferences 
continued over the next two decades. Future meetings were 
the battlegrounds for the great controversy of the quantum 
theory. Here in Brussels, at the later conferences, Bohr and 
Einstein argued over the philosophical and physical implica- 
tions of quantum mechanics. 

Einstein had admired Bohr since the publication of Bohr's 
first paper on the quantum theory of atoms in 1913. In April 
1920, Bohr came to Berlin to deliver a series of lectures. Ein- 
stein held a position in that city with the Prussian Academy 
of Science. The two men met, and Bohr spent some time with 
the Einsteins at their home. He had brought them gifts: good 
Danish butter and other foodstuffs. Einstein and Bohr 
enjoyed engrossing conversations on radiation and atomic 
theory. After Bohr left, Einstein wrote him: "Seldom in my 
life has a person given me such pleasure by his mere pres- 
ence as you have. I am now studying your great publications 
and — unless I happen to get stuck somewhere — have the 
pleasure of seeing before me your cheerful boyish face, smil- 
ing and explaining." 17 



ENTER EINSTEIN © III 

Over the years, their relationship matured into an amica- 
ble competition for the truth about nature. Bohr, the ortho- 
dox interpreter of the quantum theory, was defending its 
curious facets, while Einstein, the realist, was ever pushing 
for a more "natural" theory — one which, alas, neither he nor 
anyone else was able to produce. 

The debate between Einstein and Bohr on the interpreta- 
tion of quantum mechanics began in earnest during the fifth 
Solvay Conference in October 1927. All the founders of the 
quantum theory were there: Planck, Einstein, Bohr, de 
Broglie, Heisenberg, Schrodinger, Dirac. During the meet- 
ings, "Einstein said hardly anything beyond presenting a very 
simple objection to the probability interpretation . . . .Then 
he fell back into silence." 18 But in the dining room of the 
hotel, Einstein was very lively. According to a firsthand 
account by Otto Stern, "Einstein came down to breakfast 
and expressed his misgivings about the new quantum theory. 
Every time, he had invented some beautiful [thought] exper- 
iment from which one saw that it did not work. Pauli and 
Heisenberg, who were there, did not react well to these mat- 
ters, 'ach was, das stimmt schon, das stimmt schon' ('ah well, 
it will be all right, it will be all right'). But Bohr, on the other 
hand, reflected on it with care, and in the evening, at dinner, 
we were all together and he cleared up the matter in detail." 19 

Heisenberg, an important participant in the 1927 confer- 
ence, also described the debate: "The discussions were soon 
focused to a duel between Einstein and Bohr on the question 
as to what extent atomic theory in its present form could be 
considered to be the final solution of the difficulties which 
had been discussed for several decades. We generally met 



Ill C® ENTANGLEMENT 



already at breakfast in the hotel, and Einstein began to 
describe an ideal experiment which he thought revealed the 
inner contradictions of the Copenhagen interpretation." 20 

Bohr would work all day to find an answer to Einstein, 
and by late afternoon he would show his argument to his fel- 
low quantum theorists. At dinner, he would show Einstein his 
answer to Einstein's objection of the morning. Although Ein- 
stein would find no good objection to the argument, in his 
heart he remained unconvinced. According to Heisenberg, 
Einstein's good friend Paul Ehrenfest (1880-1933) told him: 
"I am ashamed of you. You put yourself in the same position 
as your opponents in their futile attempts to refute your rel- 
ativity theory." 

The arguments for and against the quantum theory inten- 
sified during the next Solvay Conference, which took place in 
1930. The topic of the meeting was magnetism, but that did 
not prevent the participants from continuing their heated 
debate of the quantum theory outside the regular sessions, in 
corridors, and at the breakfast and dinner tables at the hotel. 
Once, at breakfast, Einstein told Bohr that he had found a 
counterexample to the uncertainty principle for energy and 
time. Einstein envisioned an ingenious, complex device: a 
box with an opening in one of its walls, where a door is 
placed, controlled by a clock inside the box. The box is filled 
with radiation and weighed. The door is opened for a split 
second, allowing one photon to escape. The box is again 
weighed. From the weight difference, one can deduce the 
energy of the photon by using Einstein's formula, E=mc 2 . 
Thus, argued Einstein, in principle one can determine to any 
level of accuracy both the photon's energy and its time of 



ENTER EINSTEIN o JJ3 

passage, refuting the uncertainty principle (which says, in 
this context, that you cannot know both the time of passage 
and the energy to high precision). Einstein's device is shown 
below. 




As reported by Pais (1991), participants at the conference 
found Bohr in shock. He did not see a solution to Einstein's 
challenge to quantum theory. During that entire evening he 
was extremely unhappy, going from one person to the next, 
trying to persuade them that Einstein's conclusion could not 
be true: but how? If Einstein was right, Bohr said, it would 



114 c ® ENTANGLEMENT 

be the end of physics. Hard as he tried, however, he could not 
refute Einstein's clever argument. Leon Rosenfeld (1904- 
1974), a physicist present at the meetings, said: "I shall never 
forget the sight of the two antagonists leaving the club: Ein- 
stein a tall majestic figure, walking quietly, with a somewhat 
ironical smile, and Bohr trotting near him, very excited .... 
The next morning came Bohr's triumph." 21 

There is a picture that captures this description very well 
(See the first photograph, page 131.) 

Bohr finally found a flaw in Einstein's argument. Einstein 
had failed to take account of the fact that weighing the box 
amounts to observing its displacement within the gravita- 
tional field. The imprecision in the displacement of the box 
generates an uncertainty in the determination of the mass — 
and hence the energy — of the photon. And when the box is 
displaced, so is the clock inside it. It now ticks in a gravita- 
tional field that is slightly different from the one it was in 
initially. The rate of ticking of the clock in the new position 
is different from its rate before it was moved by the weigh- 
ing process. Thus there is an uncertainty in the determination 
of time. Bohr was able to prove that the uncertainty rela- 
tionship of energy and time was exactly as stated by the 
uncertainty principle. 

Bohr's answer to Einstein's challenge was brilliant, and it 
used Einstein's own general theory of relativity in parrying 
the attack. The fact that clocks tick at different rates depend- 
ing on the gravitational field is an important facet of general 
relativity. Here Bohr used a clever argument in applying rel- 
ativity theory to establish the quantum-mechanical uncer- 
tainty principle. 



ENTER EINSTEIN Co II J 

But the controversy raged on. Einstein, the wily fox of 
physics, kept coming up with increasingly more clever argu- 
ments in an effort to combat a theory whose very foundation 
he found upsetting. And since, as one of its founders, he 
knew quantum theory better than anyone, he knew how to 
deal his blows. Whenever Einstein would strike, Bohr would 
get upset and worry and frantically search for an answer until 
one was found. He would often repeat a word to himself 
while lost in thought. Fellow physicists reported him stand- 
ing in a room, muttering: "Einstein . . . Einstein . . . ," walk- 
ing over to the window, looking out, lost in thought, and 
continuing: "Einstein . . . Einstein . . . ." 

Einstein attended the 1933 Solvay Conference, and heard 
Bohr give a talk about the quantum theory. He followed the 
argument attentively, but did not comment on it. When the 
discussion began, he led it in the direction of the meaning of 
quantum mechanics. As Rosenfeld described it, Einstein "still 
felt the same uneasiness as before ('unbehagen' was the word 
he used) when confronted with the strange consequences of 
the theory." 22 It was during this occasion that he first brought 
out what would later be seen as his most formidable weapon 
against the quantum theory. "What would you say of the fol- 
lowing situation?" he asked Rosenfeld. "Suppose two parti- 
cles are set in motion towards each other with the same, very 
large, momentum, and that they interact with each other for 
a very short time when they pass at known positions. Con- 
sider now an observer who gets hold of one of the particles, 
far away from the region of interaction, and measures its 
momentum; then, from the conditions of the experiment, he 
will obviously be able to deduce the momentum of the other 



Il6 C® ENTANGLEMENT 

particle. If, however, he chooses to measure the position of 
the first particle, he will be able to tell where the other par- 
ticle is. This is a perfectly correct and straightforward deduc- 
tion from the principles of quantum mechanics; but is it not 
very paradoxical? How can the final state of the second par- 
ticle be influenced by a measurement performed on the first, 
after all physical interaction has ceased between them?" 

Here it was, two years before it was unleashed on the 
world of science with all its might — Einstein's tremendously 
potent idea about quantum theory, in which he used the 
theory's apparent contradictions to invalidate itself. Rosen- 
feld, with whom Einstein shared his thought while listening 
to Bohr's presentation, did not think that Einstein meant 
more by this thought experiment than an illustration of an 
unfamiliar feature of quantum mechanics. But the spark of 
the idea Einstein first formulated during Bohr's presentation 
would continue to grow and would take its final form two 
years later. 

When Hitler came to power, Albert Einstein left Germany. 
Already in 1930, Einstein had spent considerable portions of 
his time abroad: he was at Caltech in California, and later at 
Oxford University. In 1933, Einstein accepted a position at 
the newly established Institute for Advanced Study at Prince- 
ton. He had planned to spend some of his time there and 
some of it in Berlin, but following Hitler's victory, he quit all 
his appointments in Germany and vowed never to return. He 
spent some time in Belgium and England, and finally arrived 
at Princeton in October 1933. 

Einstein settled in his new position at the Institute for 
Advanced Study. He was given an assistant, a twenty-four 



ENTER EINSTEIN <© IIJ 

year old American physicist named Nathan Rosen (1910- 
1995). And he was reacquainted with a physicist at the Insti- 
tute whom he had known at Caltech three years earlier, Boris 
Podolsky. Einstein may have moved across the Atlantic, thou- 
sands of miles away from the Europe in which the quantum 
theory was born and developed, but the outlandish theory 
with its incomprehensible logic and assumptions remained 
on his mind. 

Einstein had usually worked alone, and his papers were 
rarely coauthored. But in 1934, he enlisted the help of Podol- 
sky and Rosen in writing one last polemic against the quan- 
tum theory. 23 Einstein later explained how the now-famous 
Einstein, Podolsky, and Rosen (EPR) paper was written in a 
letter to Erwin Schrodinger the following year: "For linguis- 
tic reasons, the paper was written by Podolsky, after pro- 
longed discussions. But what I really wanted to say hasn't 
come out so well; instead, the main thing is, as it were, buried 
under learning." Despite Einstein's impression to the con- 
trary, the message of the EPR article, in which he and his col- 
leagues used the concept of entanglement to question the 
completeness of the quantum theory, was heard loud and 
clear around the world. In Zurich, Wolfgang Pauli (1900- 
1958), one of the founders of the quantum theory and the 
discoverer of the "exclusion principle" for atomic electrons, 
was furious. He wrote a long letter to Heisenberg, in which 
he said: "Einstein has once again expressed himself publicly 
on quantum mechanics, indeed in the 15 May issue of Phys- 
ical Review (together with Podolsky and Rosen — no good 
company, by the way). As is well known, every time that hap- 
pens it is a catastrophe." Pauli was upset that the EPR paper 



ENTANGLEMENT 



was published in an American journal, and he was worried 
that American public opinion would turn against the quan- 
tum theory. Pauli suggested that Werner Heisenberg, whose 
uncertainty principle bore the brunt of the EPR paper, issue 
a quick rejoinder. 

But in Copenhagen, the response was the most pro- 
nounced. Niels Bohr seemed as if hit by lightning. He was in 
shock, confused, and he was angry. He withdrew and went 
home. According to Pais, Rosenfeld was visiting Copenhagen 
at that time, and said that the next morning, Bohr appeared 
at his office all smiles. He turned to Rosenfeld and said: 
"Podolsky, Opodolsky, Iopodolsky, Siopodolsky, Asiopodol- 
sky, Basiopodolsky . ..." To the bewildered physicist he 
explained that he was adapting a line from the Holberg play 
Ulysses von Ithaca (Act I, Scene 15), in which a servant sud- 
denly starts to talk gibberish. 24 

Rosenfeld recalled that Bohr abandoned all the projects he 
was working on when the EPR paper came out. He felt the 
misunderstanding had to be cleared up as quickly as possible. 
Bohr suggested that he and his helpers use the same example 
that Einstein used to demonstrate the "right" way to think 
about it. Bohr, excited, began to dictate to Rosenfeld the 
response to Einstein. But soon, he hesitated: "No, this won't 
do ... we have to do this all over again ... we must make it 
quite clear . . . ." According to Rosenfeld, this went on for 
quite a while. Every once in a while, Bohr would turn to 
Rosenfeld: "What can they mean? Do you understand it?" 
He would toss the ideas in his mind, getting nowhere. Finally, 
he said he "must sleep on it." 25 

Over the next few weeks, Bohr calmed down enough to 



ENTER EINSTEIN & IK) 

write his rebuttal to the Einstein-Podolsky-Rosen paper. 
Three months of hard work later, Bohr finally submitted his 
response to Einstein and his colleagues to the same journal 
that had published the EPR paper, Physical Review. He 
wrote, in part (the italics are his): " We are in the freedom of 
choice offered by [EPR], just concerned with a discrimination 
between different experimental procedures which allow of 
the unambiguous use of complementary classical concepts." 
But not all physicists saw the situation this way. Erwin 
Schrodinger, whose theory was challenged by EPR, told Ein- 
stein: "You have publicly caught dogmatic quantum mechanics 
by its throat." Most scientists were either convinced by Bohr's 
reply to EPR, or else thought that the controversy was philo- 
sophical rather than physical, since experimental results were 
not in question, and hence beyond their concern. Three decades 
later, Bell's theorem would undermine this point of view. 

WHAT DOES THE EPR PAPER SAY? 

According to Einstein, Podolsky, and Rosen, any attribute of 
a physical system that can be predicted accurately without 
disturbing the system is an element of physical reality. 

Furthermore, EPR argue, a complete description of the 
physical system under study must embody all the elements of 
physical reality that are associated with the system. 

Now, Einstein's example (essentially the same one he told 
Rosenfeld two years earlier) of two particles that are linked 
together shows that the position and momentum of a given 
particle can be obtained by the appropriate measurements 
taken of another particle without disturbing its "twin." Thus 
both attributes of the twin are elements of physical reality. 



120 C® ENTANGLEMENT 



Since quantum mechanics does not allow both to enter the 
description of the particle, the theory is incomplete. 

The EPR paper (along with Bell's theorem, which followed 
it) is one of the most important papers in twentieth-century 
science. "If, without in any way disturbing a system ," it 
declares, "we can predict with certainty (i.e., with probabil- 
ity equal to unity) the value of a physical quantity, then there 
exists an element of physical reality corresponding to this 
physical quantity. It seems to us that this criterion, while far 
from exhausting all possible ways of recognizing a physical 
reality, at least provides us with one such way, whenever the 
conditions set down in it occur." 26 

EPR then embark on a description of entangled states. 
These entangled states are complicated, because they use 
both position and momentum of two particles that have 
interacted in the past and thus are correlated. Their argu- 
ment is basically a description of quantum entanglement for 
position and momentum. Following this description, EPR 
conclude: 

"Thus, by measuring either A or B we are in a position to 
predict with certainty, and without in any way disturbing the 
second system, either the value of the quantity P or the value 
of the quantity Q. In accordance with our criterion for real- 
ity, in the first case we must consider the quantity P as being 
an element of reality, in the second case the quantity Q is an 
element of reality. But as we have seen, both wave functions 
belong to the same reality. Previously we proved that either 
(1) the quantum-mechanical description of reality given by 
the wave function is not complete or (2) when the operators 
corresponding to the two physical quantities do not com- 



ENTER EINSTEIN © 121 

mute the two quantities cannot have simultaneous reality. . . . 
We are thus forced to conclude that the quantum-mechani- 
cal description of physical reality given by wave functions is 
not complete." 

What Einstein and his colleagues did was to make what 
seems like a very reasonable assumption, the assumption of 
locality. What happens in one place does not immediately 
affect what happens in another place. EPR say: "If, without 
in any way disturbing a system, we can predict with certainty 
(i.e., with probability equal to unity) the value of a physical 
quantity, then there exists an element of physical reality cor- 
responding to this physical quantity." This condition is sat- 
isfied when a measurement of position is made on particle 1 
and also when a measurement of momentum is made of the 
same particle. In each case, we can predict with certainty the 
position (or momentum) of the other particle. This permits us 
the inference of the existence of an element of physical real- 
ity. Now, since particle 2 is unaffected (they assume) by what 
is done to particle 1, and the element of reality — the posi- 
tion — of this particle is inferred in one case, and of momen- 
tum in the other, both position and momentum are elements 
of physical reality of particle 2. Thus the EPR "paradox." 
We have two particles that are related to each other. We mea- 
sure one and we know about the other. Thus, the theory that 
allows us to do that is incomplete. 

In his response, Bohr said: "The trend of their [EPR] argu- 
mentation, however, does not seem to me adequately to meet 
the actual situation with which we are faced in atomic 
physics." He argued that the EPR "paradox" did not present 
a practical challenge to the application of quantum theory to 



J22 Cs ENTANGLEMENT 

real physical problems. Most physicists seemed to buy his 
arguments. 

Einstein came back to the problem of EPR in articles writ- 
ten in 1948 and 1949, but he spent most of the remaining 
time until his death in 1955 trying, unsuccessfully, to develop 
a unified theory of physics. He never did come around to 
believing in a dice-playing God — he never did believe that 
quantum mechanics with its probabilistic character was a 
complete theory. There was something missing from the 
theory, he thought, some missing variables that could explain 
the elements of reality better. The conundrum remained: Two 
particles were associated with each other — twins produced 
by the same process — forever remaining interlinked, their 
wave function unfactorable into two separate components. 
Whatever happened to one particle would thus immediately 
affect the other particle, wherever in the universe it may be. 
Einstein called this "Spooky action at a distance." 

Bohr never forgot his arguments with Einstein. He talked 
about them until the day of his death in 1962. Bohr fought 
hard to have quantum theory accepted by the world of sci- 
ence. He countered every attack on the theory as if it had 
been a personal one. Most physicists thought that Bohr had 
finally settled the issue of quantum theory and EPR. But two 
decades later Einstein's argument was to be revived and 
improved by another physicist. 



12 

Bohm and Aharonov 



"The most fundamental theory now available is proba- 
bilistic in form, and not deterministic." 

— David Bohm 



David Bohm was born in 1917, and studied at the 
I University of Pennsylvania, and later at the Uni- 
versity of California at Berkeley. He was a student 
of Robert Oppenheimer until Oppenheimer left Berkeley to 
head the Manhattan Project. Bohm finished his doctorate at 
Berkeley and then accepted a position at Princeton University. 
At Princeton, David Bohm worked on the philosophy of 
quantum mechanics, and in 1952 made a breakthrough in 
our understanding of the EPR problem. Bohm changed the 
setting of Einstein's challenge to quantum theory — the EPR 
paper — in a way that made the issues involved in the "para- 
dox" much clearer, more concise, and easier to understand. 
Instead of using momentum and position — two elements — in 
the EPR preparation, Bohm changed the thought experiment 
to one involving two particles with one variable of interest 



123 



124 c ® ENTANGLEMENT 

instead of two, the physical element of interest being the spin 
associated with each of the two particles along a particular 
direction. In the Bohm formulation, as in the original EPR 
arrangement, both particles can be localized at a distance 
from each other, so that spin measurements on each are sep- 
arated in space and time without a direct effect on each other. 

Some particles, electrons for example, have a spin associ- 
ated with them. The spin can be measured independently in 
any direction the experimenter may choose. Whichever axis 
is chosen, the experimenter gets an answer of either: "spin 
up," or "spin down" when a spin measurement is made. 
When two particles are entangled with each other in what is 
called a singlet state, in which the total spin must be zero, 
their spin is inexorably linked: if one particle shows spin up, 
the other will show spin down. We don't know what the spin 
is, and according to quantum theory the spin is not a definite 
property until it is measured (or otherwise actualized). Two 
particles fly off from the same source that made them entan- 
gled, and they move away from each other. Particle "A" is 
measured some time later by Alice, who arbitrarily chooses 
to measure the particle's spin in, say, the x-direction. Accord- 
ing to quantum theory, once particle "A" reveals a spin of 
"up" in the x-direction, particle "B," if measured by Bob in 
the x-direction will reveal a "down" spin. The same anti-cor- 
relation holds if Alice and Bob choose to measure spin in any 
other direction, say, the y-direction. (One needs two such 
directions in order to make the EPR argument using spins.) 

In the Bohm version of the EPR thought experiment, two 
entangled particles are emitted. Once the spin of one of them 
is measured, and is found to be "up," the spin of the other 



BOHM AND AHARONOV C© J2j" 

one must be "down," and this must be so for all directions, 
for example, both x and y. According to quantum mechan- 
ics, the value of the spin in different directions does not have 
simultaneous reality. But EPR's argument was that all of 
these are real. Bohm's alteration of the EPR thought experi- 
ment simplified the analysis greatly. The Bohm version of the 
EPR thought experiment is shown below. 




In 1949, Bohm was investigated by the House Committee 
on Un-American Activities, during the heart of the McCarthy 
era. Bohm refused to answer questions, but was not charged. 
However, he lost his position at Princeton University, and as 
a consequence left the United States to take up a position in 
Sao Paolo, Brazil. From there he moved for a while to Israel, 
and then to England, where he became a professor of theo- 
retical physics at the University of London. Bohm continued 
to work in the foundations of quantum theory, and his dis- 
coveries led to an alternative to the "orthodox," Copenhagen 
view of the discipline. 

In 1957, Bohm and Yakir Aharonov of the Technion in 



126 C® ENTANGLEMENT 

Haifa, Israel, wrote a paper recalling and describing the 
experiment of Wu and Shaknov that exhibited the spin cor- 
relations of Bohm's version of the EPR paradox. The paper 
argued against the view that perhaps the particles are not 
really entangled or that the quantum entanglement of parti- 
cles might dissipate with distance. All the experiments that 
have been conducted since then confirm this view: the entan- 
glement of particles is real and does not dissipate with 
increasing separation. 

In 1959, Bohm and Aharonov discovered what is now 
called the Aharonov-Bohm effect, which made them both 
famous. The Aharonov-Bohm effect is a mysterious phe- 
nomenon, which, like entanglement, possesses a non-local 
character. Bohm and Aharonov discovered a phase shift in 
electron interference due to an electromagnetic field that has 
zero field strength along the path of the electron. What this 
means is that even if we have a cylinder within which there 
is an electromagnetic field, but the field is limited to the inte- 
rior of the cylinder, an electron passing outside the cylinder 
will still feel the effects of the electromagnetic field. Thus, an 
electron that passes outside the cylinder containing the mag- 
netic field will still — mysteriously — be affected by the field 
inside the cylinder. This is demonstrated in the figure below. 



Closed 
Cylinder 



Magnetic field confined to 
the insides of the cylinder 



BOHM AND AHARONOV C© 1ZJ 



I 
• e- 

i 
i 
i 

i 



The electron feels the effects 

of the magnetic field confined 

to the cylinder 



Like other mysteries of quantum mechanics, no one really 
understands "why" this happens. The effect is similar to 
entanglement in the sense that it is non-local. Bohm and 
Aharonov deduced this effect from theoretical, mathematical 
considerations. Years later, the Aharonov-Bohm effect was 
verified experimentally. 



Bohm's contributions to our understanding of quantum 
theory and entanglement are important. His version of the 
EPR thought experiment would be the one most often used 
by experimentalists and theorists studying entanglement in 
the following decades. 

In addition, an important requirement for tests of the EPR 
paradox was laid out by Bohm and Aharonov in 1957. They 
claimed that in order to find out whether the EPR particles 
behaved in the way Einstein and his colleagues found objec- 
tionable, one would have to use a delayed-choice mechanism. 
That is, an experimenter would have to choose which spin 



128 & ENTANGLEMENT 



direction to measure in the experiment only after the parti- 
cles are in flight. Only this design would ensure that one par- 
ticle, or the experimental apparatus, does not signal to the 
other particle what is going on. This requirement would be 
emphasized by John Bell, whose theorem would change our 
perceptions of reality. An important experimenter would add 
this requirement to his tests of Bell's theorem, helping estab- 
lish the fact that entanglement of particles that are remote 
from each other is a real physical phenomenon. 




Niels Bohr and 
Albert Einstein at 
the 1930 Solvay 
Conference. 

Courtesy the Niels Bohr 
Archive, Copenhagen. 



Niels Bohr and Werner 

Heisenberg in the 

Tyrol, 1932. 

Courtesy the Niels Bohr 
Archive, Copenhagen. 





Heisenberg and Bohr at the 1936 Copenhagen Conference. 

Courtesy the Niels Bohr Archive, Copenhagen. 




Niels Bohr with Max Planck, in Copenhagen, 1930. 

Courtesy the Niels Bohr Archive, Copenhagen. 1921. 




Max Planck in 1921. 

Courtesy the Niels Bohr Archive, Copenhagen. 




Erwin Schrodinger. 

Courtesy the Niels Bohr Archive, Copenhagen. 




(R to L) D. Greenberger, M. Home, and A. Zeilinger in front 
of the GHZ experimental design at Anton Zeilinger's lab in 
Vienna. 

Courtesy Anton Zeilinger. 




P.K. Aravind. 

Courtesy Amir Aczel. 




Alain Aspect in his office in Orsay, France. 

Courtesy Amir Aczel. 




Carol and Michael Home, Anton and Elisabeth Zeilinger, in 
Cambridge, MA, in 2001. 

Courtesy Amir Aczel. 




Abner Shimony. 

Courtesy Amir Aczel. 




John Archibald Wheeler (right) with the author on the deck 
of Wheeler's house in Maine. 

Courtesy Debra Gross Aczel. 



13 

John BelVs Theorem 



"For me, then, this is the real problem with quantum 
theory: the apparently essential conflict between any sharp 
formulation and fundamental relativity. It may be that a 
real synthesis of quantum and relativity theories requires 
not just technical developments but radical conceptual 
renewal." 

—John Bell 



M ohn S. Bell, a redheaded, freckled man who was quiet, 
m polite, and introspective, was born in Belfast, Northern 
m Ireland, in 1928 to a working-class family whose mem- 
** bers were blacksmiths and farmers. His parents were John 
and Annie Bell, both of whose families had lived in Northern 
Ireland for generations. John's middle name, Stewart, was 
the Scottish family name of John's mother, and at home John 
was called Stewart until the time he went to college. The Bell 
family was Anglican (members of the Church of Ireland), but 
John cultivated friendships that went beyond religion or eth- 
nicity, and many of his friends were members of the Catholic 
community. Bell's parents were not rich, but they valued edu- 
cation. They worked hard to save enough money to send 
John to school, even though his siblings left school early to 
begin work. Eventually, his two brothers educated them- 



137 



138 C© ENTANGLEMENT 

selves, and one became a professor and the other a success- 
ful businessman. 

When he was 11, John, who read extensively, decided that 
he wanted to become a scientist. He succeeded very well in 
the entrance exams for secondary education, but unfortu- 
nately his family could not afford to send him to a school 
with an emphasis on science, and John had to content him- 
self with admission to the Belfast Technical High School, 
where he was educated both academically and in practical 
areas. He graduated in 1944 at the age of 16, and found a job 
as a technical assistant in the physics department of Queen's 
University in Belfast. There, he worked under the supervi- 
sion of Professor Karl Emeleus, who recognized his assis- 
tant's great talent in science and lent him books and even 
allowed him to attend freshman courses without being for- 
mally enrolled at the university. 

After a year as a technician, John was accepted at the uni- 
versity as a student and was awarded a modest scholarship, 
which allowed him to pursue a degree in physics. He gradu- 
ated in 1948 with a degree in experimental physics, and 
stayed another year, at the end of which he was awarded a 
second bachelor's degree, this time in mathematical physics. 
John was fortunate to study with the physicist Paul Ewald, a 
gifted German refugee, who was a pioneer in the area of X- 
ray crystallography. John excelled in physics, but was 
unhappy with the way the quantum theory was explained at 
the university. His deep mind understood that there were 
some mysteries in this theory that had not been addressed in 
the classroom. He did not know, at the time, that these unex- 
plained ideas were not understood by anyone, and that it 



JOHN BELL'S THEOREM & 139 

would be his own work that in time would shed light on 
these problems. 

After working for some time at a physics laboratory at 
Queen's College in Belfast, Bell entered the University of 
Birmingham, where he received his Ph.D. in physics in 1956. 
He specialized in nuclear physics and quantum field theory, 
and after receiving his degree he worked for several years at 
the British Atomic Energy Agency. 

While doing research on accelerator physics at Malvern in 
Britain, John met Mary Ross, a fellow accelerator physicist. 
They were married in 1954, and pursued careers together, 
often working on the same projects. After they both had 
earned their doctoral degrees (she received hers in mathe- 
matical physics from the University of Glasgow) and worked 
for several years at Harwell for the British nuclear establish- 
ment, they both became disenchanted with the direction the 
nuclear research center was taking; they resigned their 
tenured positions at Harwell to assume non-tenured posts at 
the European Center for Nuclear Research (CERN) in 
Geneva. There, John worked at the Theory Division, and 
Mary was a member of the Accelerator Research Group. 

Everyone who knew him was struck by John Bell's bril- 
liance, intellectual honesty, and personal modesty. He pub- 
lished many papers and wrote many important internal 
memos, and it was clear to everyone who knew him that his 
was one of the greatest minds of the era. Bell had three sep- 
arate careers: one was the study of the particle accelerators 
with which he worked; another was the theoretical particle 
physics he did at CERN; and the third career — the one which 
ultimately made his name famous beyond the community of 



140 Cs ENTANGLEMENT 

physicists — was in the fundamental concepts of quantum 
mechanics. At conferences organized around him, people 
congregated who were in the three disciplines John followed, 
but did not know of each other. Apparently he kept his three 
careers separate, so people in one discipline did not know he 
was involved in the other two. 

John Bell's working hours at CERN were devoted almost 
exclusively to theoretical particle physics and accelerator 
design, so that only his spare time at home could be used to 
pursue what he called his "hobby" — exploring the basic ele- 
ments of the quantum theory. In 1963, he took a year's leave 
from CERN and spent it at Stanford, the University of Wis- 
consin, and Brandeis University. It was during this year 
abroad that John began to address the problems at the heart 
of quantum theory in a serious way. He continued his work 
on these issues after returning to CERN in 1964, but was 
careful to keep his involvement with the quantum theory sep- 
arate from his "main" career at CERN doing particle and 
accelerator research. The reason was that John Bell had 
understood early on in his career the serious pitfalls in the 
quantum theory. While on leave in the U.S., Bell made a 
breakthrough that told him that John von Neumann had 
made an error with his assumptions about quantum theory, 
but, in Bell's words, "I walked away from the problem." 

There was no question in anyone's mind that John von 
Neumann was a superb mathematician — probably a genius. 
And Bell had no issue with von Neumann's mathematics. It 
was the interface between mathematics and physics that gave 
him trouble. In his groundbreaking book on the foundations 
of quantum theory, von Neumann had made one assump- 



JOHN BELL'S THEOREM C® 141 

tion — which was essential to what came after it — that did 
not make good physical sense, as John Bell saw it. Von Neu- 
mann assumed in his work on quantum theory that the 
expected value (the probability-weighted average) of the sum 
of several observable quantities was equal to the sum of the 
expected values of the separate observable quantities. [Math- 
ematically, for observable quantities A, B, C, . . . , and expec- 
tation operator £( ), von Neumann thought it was natural to 
take: E(A + B + C + . . . ) = E(A ) + E(B ) + E(C ) + . . . .] John 
Bell knew that this innocuous-looking assumption was not 
physically defensible when the observables A, B, C, . . . are 
represented by operators that do not necessarily commute 
with one another. Put roughly in a non-mathematical lan- 
guage, von Neumann had somehow abandoned the uncer- 
tainty principle and its consequences, since non-commuting 
operators cannot be measured at once without loss in preci- 
sion due to the uncertainty principle. 

John Bell wrote his first important paper on quantum fun- 
damentals, which was published as his second paper in this 
area in 1966 (a later, related paper, which we will discuss 
soon, being published first). In this paper, "On the Problem 
of Hidden Variables in Quantum Mechanics," he addressed 
the error in von Neumann's work as well as similar difficul- 
ties with the works of Jauch and Piron, and Andrew Gleason. 

Gleason is a mathematician as renowned as von Neumann 
was. He is a professor at Harvard University who made his 
name solving one of Hilbert's famous problems. In 1957, 
Andrew Gleason wrote a paper about projection operators in 
Hilbert space. Unbeknownst to Bell, Gleason's theorem was 
relevant to the problem of hidden variables in quantum 



J4^ Cs ENTANGLEMENT 

mechanics. Josef Jauch, who lived for a time in Geneva, 
where John and Mary Bell lived, brought Gleason's theorem 
to the attention of John Bell while he was in the process of 
researching his paper on hidden variables. Gleason's theo- 
rem has a certain generality and it is not aimed at solving 
problems in the quantum theory — it was proved by a pure 
mathematician with interest in mathematics and not physics. 
The theorem, however, has a remarkable corollary with 
important implications to quantum mechanics. The corol- 
lary of Gleason's theorem implies that no system associated 
quantum-mechanically with a Hilbert space with dimension 
three or greater can admit a dispersion-free state. Bell 
noticed, however, that if one weakens Gleason's premises, 
then there is a possibility of a more general kind of hidden- 
variables theory, a class of theories that today are known as 
"contextual" hidden-variables theories. Thus there was a 
loophole if one tried to use Gleason's theorem within the 
context of the EPR idea. 

Dispersion-free states are states that can have precisely 
measured values. They have no variation, no dispersion, no 
uncertainty. If dispersion-free states do exist, then the preci- 
sion they entail comes from some missing, hidden variables, 
because quantum theory admits an uncertainty principle. 
Thus to get away from the remaining uncertainty inherent in 
quantum mechanics in order to achieve these precise, dis- 
persion-free states, one would have to use hidden variables. 

Bell didn't understand Gleason's proof of the corollary of 
his theorem, so he came up with his own proof that showed 
that except for the unimportant case of a two-dimensional 
Hilbert space, there are no dispersion-free states, hence no 



JOHN BELL'S THEOREM C® 143 

hidden variables. In the case of von Neumann, Bell proved 
that the assumption used by von Neumann was inappropri- 
ate and hence that his results were questionable. Having 
revived the argument about whether hidden variables exist in 
the quantum theory, Bell went a step further: he attacked the 
problem of EPR and entanglement. 

Bell had read the 1935 paper by Einstein and his two col- 
leagues, Podolsky and Rosen (EPR), which was published 30 
years earlier as a challenge to the quantum theory. Bohr and 
others had responded to the paper, and everyone else in 
physics believed that the issue had been closed and that 
Einstein was shown to have been wrong. But Bell thought 
otherwise. 

John Bell recognized an immense truth about the old EPR 
argument: he knew that Einstein and his colleagues were 
actually correct. The "EPR Paradox," as everyone had called 
it, was not a paradox at all. What Einstein and his colleagues 
found was something crucial to our understanding of the 
workings of the universe. But it wasn't the claim that the 
quantum theory was incomplete — it was that quantum 
mechanics and Einstein's insistence on realism and locality 
could not both be right. If the quantum theory was right, 
locality was not; and if we insist on locality, then there is 
something wrong with the quantum theory as a description 
of the world of the very small. Bell wrote this conclusion in 
the form of a deep mathematical theorem, which contained 
certain inequalities. He suggested that if his inequalities could 
be violated by the results of experimental tests, such a viola- 
tion would provide evidence in favor of quantum mechanics, 
and against Einstein's common-sense assumption of local 



144 c ® ENTANGLEMENT 

realism. If the inequalities were preserved, it would prove 
that the quantum theory, in turn, was wrong and that local- 
ity — in the sense of Einstein — was the right viewpoint. More 
precisely, it is possible to violate both Bell's inequalities and 
the predictions of quantum mechanics, but it is impossible to 
obey both Bell's inequalities and the predictions of quantum 
mechanics for certain quantum states. 

John Bell wrote two groundbreaking papers. The first paper 
analyzed the idea of von Neumann and others about the exis- 
tence of hidden variables, which should be found and added 
to the quantum theory in order to render it "complete," as 
Einstein and his colleagues had demanded. In the paper, John 
Bell proved that von Neumann's and others' theorems prov- 
ing the impossibility of the existence of hidden variables in 
quantum mechanics were all flawed. Then Bell proved his 
own theorem, establishing, indeed, that hidden variables 
could not exist. Because of a delay in publication, this first 
important paper by Bell was published in 1966, after the 
appearance of his second paper. The second paper, published 
in 1964, was titled "On the Einstein-Podolsky-Rosen Para- 
dox." This paper included the seminal "Bell's Theorem," 
which changed the way we think about quantum phenomena. 

Bell used a particular form of the EPR paradox, one that 
had been refined into an easier form by David Bohm. He 
looked at the case in which two entangled spin- 1/2 particles 
in the singlet state are emitted from a common source, and 
analyzed what happens in such an experiment. 

In the paper, Bell said that the EPR paradox has been 
advanced as an argument that quantum theory could not be 
complete and must be supplemented by additional variables. 



JOHN BELL'S THEOREM C® 145 

Such additional variables, according to EPR, would restore 
to quantum mechanics its missing notions of causality and 
locality. In a note, Bell quoted Einstein: 27 

But on one supposition we should, in my opinion, absolutely 
hold fast: the real factual situation of the system S 2 is inde- 
pendent of what is done with the system S 13 which is spatially 
separated from the former. 

Bell stated that in his paper he would show mathematically 
that Einstein's ideas about causality and locality are incom- 
patible with the predictions of quantum mechanics. He fur- 
ther stated that it was the requirement of locality — that the 
result of a measurement on one system be unaffected by oper- 
ations on a distant system with which it has interacted in the 
past — that creates the essential difficulty. Bell's paper pre- 
sents a theorem of alternatives: either local hidden variables 
are right, or quantum mechanics is right, but not both. And 
if quantum mechanics is the correct description of the micro- 
world, then non-locality is an important feature of this 
world. 

Bell developed his remarkable theorem by first assuming 
that there is some way of supplementing quantum mechan- 
ics with a hidden-variable structure, as Einstein would have 
demanded. The hidden variables thus carry the missing infor- 
mation. The particles are endowed with an instruction set 
that tells them, beforehand, what to do in each eventuality, 
i.e., in each choice of the axis with respect to which the spin 
might be measured. Using this assumption, Bell obtained a 
contradiction, which showed that quantum mechanics could 
not be supplemented with any hidden-variables scheme. 



146 



ENTANGLEMENT 



Bell's theorem puts forward an inequality. The inequality 
compares the sum, denoted by S, of possible results of the 
experiment — outcomes on the detector held by Alice, and the 
one held by Bob. 

Bell's inequality is: -2 < S < 2 

The inequality is shown below. 
S 



Angle 




According to Bell's theorem, if the inequality above is vio- 
lated, that is, the sum of the particular responses for Alice 
and Bob is greater than two or less than minus two, as a 
result of some actual experiment with entangled particles or 
photons, that result constitutes evidence of non-locality, 
meaning that something that happens to one particle does 
affect, instantaneously, what happens to the second particle, 
no matter how far it may be from the first one. What 
remained was for experimentalists to look for such results. 

There was a problem here, however. Bell derived his 
inequality from a locality assumption by using a special 
hypothesis. He assumed that the hidden variables theory 
agrees exactly with the quantum-mechanical prediction for 



JOHN BELL'S THEOREM C® 14J 

the two particles in the singlet state, i.e., that along any axis, 
the spin of particle 1 is opposite to that of particle 2 along the 
same axis. Hence, if the experimental values agree with the 
quantum-mechanical prediction of the quantity in Bell's 
inequality, this finding would not imply the falsity of the 
locality assumption unless there is evidence that Bell's special 
assumption is correct, and such evidence is very hard to 
obtain in practice. This problem would constitute a barrier 
to definitive experimental testing. But Clauser, Home, Shi- 
mony, and Holt would later derive an improvement that 
would solve this technical problem and enable actual physi- 
cal testing using Bell's theorem. 

At any rate, the conclusion from Bell's theorem was that 
hidden variables and a locality assumption had no place 
within the quantum theory, which was incompatible with 
such assumptions. Bell's theorem was thus a very powerful 
theoretical result in physics. 

"Do you know why it was Bell, rather than anyone else, 
who took up the EPR paradox and proved a theorem estab- 
lishing that non-locality and quantum theory go together?" 
Abner Shimony asked me. "It was clear to everyone who 
knew him that it had to be John Bell," he continued. "Bell 
was a unique individual. He was curious, tenacious, and 
courageous. He had a stronger character than all of them. 
He took on John von Neumann — one of the most famous 
mathematicians of the century — and with no hesitation 
showed that von Neumann's assumption was wrong. Then 
he took on Einstein." 

Einstein and his colleagues found entanglement between 
spatially well-separated systems unbelievable. Why would 



148 & ENTANGLEMENT 

something occurring at one place affect instantaneously 
something at a different location? But John Bell could see 
beyond Einstein's intuition and prove the theorem that would 
inspire experiments to establish that entanglement was a real 
phenomenon. Bell antecedently agreed with Einstein, but left 
it for experiment to test whether Einstein's belief about local- 
ity was correct. 

John Bell died unexpectedly in 1990, at the age of 62, from 
a cerebral hemorrhage. His death was a great loss to the 
physics community. Bell had continued to be active to his 
last days, writing and lecturing extensively on quantum 
mechanics, the EPR thought experiment, and his own theo- 
rem. In fact, physicists today continue to look to Bell's the- 
orem, with its deep implications about the nature of 
space-time and the foundations of the quantum, as they have 
over the past three decades. Experiments connected to the 
theorem have almost all provided overwhelming support for 
the quantum theory and the reality of entanglement and non- 
locality. 



The Dream of Clauses Home, 
and Sbimony 



"Our understanding of quantum mechanics is troubled by 
the problem of measurement and the problem of nonlocal- 
ity. . . It seems to me unlikely that either problem can be 
solved without a solution to the other, and therefore with- 
out a deep adjustment of space-time theory and quantum 
mechanics to each other." 

— Abner Shimony 



^bner Shimony comes from a rabbinical Jewish family. 

/ 1 His ancestors were among the very few families to 
JL JL have lived continuously in Jerusalem for many gen- 
erations, and his great grandfather was the chief shochet 
(overseer of kosher slaughtering) of Jerusalem. Abner was 
born in Columbus, Ohio, in 1928, and grew up in Memphis, 
Tennessee. From an early age, Abner exhibited a keen intel- 
lectual curiosity. As an undergraduate, Abner went to Yale 
University to study philosophy and mathematics from 1944 
to 1948, when he received his bachelor's degree. He read 
much philosophy, including Alfred North Whitehead, 
Charles S. Pierce, and Kurt Godel. While at Yale, he also 
became interested in the foundations of mathematics. 

Shimony continued his studies at the University of 
Chicago, earning his Master's degree in philosophy, and then 



149 



I JO & ENTANGLEMENT 

went to Yale to do doctoral work in philosophy, earning his 
Ph.D. in 1953. While at the University of Chicago, Abner 
studied philosophy with the renowned central figure of the 
Vienna Circle, an elite European philosophical club, Rudolph 
Carnap, who later became his informal advisor when Abner 
was writing his doctoral dissertation at Yale on inductive 
logic. Carnap seemed baffled by the fact that despite Abner's 
interest in mathematical logic and theoretical physics he pro- 
claimed himself a metaphysician. This was an appropriate 
field of interest for him, since he would make his great mark 
both on physics and on philosophy when he would probe 
the metaphysical aspects of the concept of entanglement, 
which would become Abner's obsession and lifelong pursuit 
within a few years. 

At Princeton, Abner met another philosopher with close 
contacts with the Vienna Circle: the legendary Kurt Godel. 
Abner was impressed with the supreme mind that devised 
the famous incompleteness theorems and proved difficult 
facts about the continuum hypothesis. Shortly afterwards, 
Abner decided that he really wasn't that interested in the 
foundations of mathematics and turned his attention to 
physics and philosophy. He had become very interested in 
the philosophical foundations of physics, and so he studied 
physics and received his Ph.D. in 1962. His dissertation was 
in the area of statistical mechanics. Shimony became 
attracted to the quantum theory, and was influenced in his 
thinking by Eugene Wigner and John Archibald Wheeler. 

Shimony has always made a serious effort to combine his 
philosophical and physical interests carefully. He views 
physics from a fundamental, mathematical and philosophical 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY Co IJI 

point of view, which gives him a unique perspective on the 
entire discipline and its place within human pursuits. In 
i960, before obtaining his second doctorate, Shimony joined 
the philosophy faculty at M.I.T., teaching courses on the phi- 
losophy of quantum mechanics. He began to make a name 
for himself in this area, and after receiving his second doc- 
torate from Princeton, joined the faculty at Boston University, 
with a joint appointment in physics and philosophy. 

As Abner views it, his was not an expected career path — 
starting out at a prestigious school such as MIT, getting 
tenure there, and then switching to an untenured position at 
a somewhat lower-prestige school (tenure did come to him 
there very quickly, though). But Abner did it because he 
wanted to follow his heart. MIT had, and still has, a superb 
physics department; the institute, in fact, boasts a number of 
Nobel laureates in physics. But Abner was working within 
the philosophy department. He longed to teach and do 
research in both physics and philosophy. So he gave up his 
tenured position at MIT for a joint appointment in the 
departments of physics and philosophy at Boston University. 
The new appointment allowed him to pursue his interests. 
Our understanding of the complex phenomenon of entan- 
glement — both from a physical and a philosophical point of 
view — owes much to this move Shimony made to Boston 
University. 

In 1963, Abner wrote an important paper on the mea- 
surement process in quantum mechanics. A year later, John 
Bell wrote his own paper that challenged our understanding 
of the world. 

Abner Shimony first encountered the concept of entangle- 



I$2 & ENTANGLEMENT 

ment in 1957. That year, his new adviser at Princeton, Arthur 
Wightman, gave him a copy of the EPR paper and asked him 
if, as an exercise, he could find out what was wrong with the 
EPR argument. Shimony studied the EPR paper, but found no 
error in it. Once John Bell's theorem became known to physi- 
cists several years later, Wightman had to agree: Einstein had 
made no errors. What Einstein did was to infer the incom- 
pleteness of quantum mechanics from the conjunction of 
three premises: the correctness of certain statistical predic- 
tions of quantum mechanics, the sufficient criterion for the 
existence of an element of reality, and the assumption of 
locality. Einstein and his colleagues pointed out to us that if 
we hold on to our belief that whatever happens in one place 
cannot instantaneously affect what happens at a distant loca- 
tion, then some phenomena predicted by quantum mechan- 
ics will be found in contradiction with such assumptions. It 
was Bell's theorem, at first ignored by the physics community, 
that brought this contradiction to the surface in a way that 
could — at least in principle — be physically tested. What Bell 
showed was that even if all of the premises of EPR were cor- 
rect, with the consequence that quantum mechanics would 
have to be completed with hidden variables, no theory using 
local hidden variables (which, of course, was what EPR 
desired) would agree with all of the statistical predictions of 
quantum mechanics. This conflict makes a decisive experi- 
ment possible, at least in principle. The essence of this idea 
was already forming in Abner Shimony's mind. 

One day in 1968, Abner Shimony found at his doorstep the 
first doctoral student he was to supervise as a professor at 
Boston University's physics department. The student was 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY Co IJ3 

Michael Home. Home came to Boston after receiving his 
B.A. in physics from the University of Mississippi, and was 
excited to work with Shimony. 

Michael A. Home was born in Gulfport, Mississippi in 1943. 
When he was in high school, the Soviet Union launched the 
first spacecraft, Sputnik. This event, which had such a pro- 
found effect on the development of science in America, as 
well as so many other facets of our lives, also had a decisive 
impact on Michael Home's choice of a career path. 

Scrambling to come up with a response to the Russian first 
in space, the United States convened a council of scientists, 
the Physical Sciences Study Committee, which met at M.I.T. 
to devise ways to make America more competitive with the 
Soviet Union in science, especially physics. The thrust of the 
program was to make the United States superior in education 
in the exact sciences, and as part of its recommendations, the 
Committee commissioned physicists to write science books 
that would help prepare students in the United States to study 
physics and other sciences. Mike Home found one of the 
books written under the auspices of the Committee at a 
bookstore in Mississippi and devoured it with great excite- 
ment. The book was written by I. B. Cohen, a science histo- 
rian at Harvard, and was titled The New Physics. It was 
about Newton and his "new" physics of the 1700s. Mike 
found this to be a beautiful book; he got so much out of the 
book that he ordered the entire series of books, at 95 cents a 
volume. The Committee was apparently very successful, at 
least with Michael Home: based on what he discovered in 
these books, he decided during his junior year in high school 



IJ4 & ENTANGLEMENT 

to become a physicist. When he attended the University of 
Mississippi, he majored in physics. 

Mike was aware of the big physics centers in the United 
States, and his dream was to do graduate studies at one of 
them. While still an undergraduate student at the University of 
Mississippi, Mike Home read the well-known book by Mach 
about mechanics. The introduction to the English translation 
in the Dover edition was written by a Boston University 
physics professor, Robert Cohen. Mike was taken with the 
book and the introduction, and wondered whether he would 
someday meet Robert Cohen, so when he applied to Boston 
University, he inquired in his letter whether Professor Cohen 
was still there. Years later, after Mike Home had made his 
name as a pioneer in the foundations of physics, Robert Cohen 
confided to him that the fact that he had asked about him did, 
indeed, make a difference. Apparently Cohen was so flattered, 
that he urged the rest of the physics faculty at Boston Univer- 
sity to accept Home to the program in 1965. 

Michael Home was attracted to the foundations of physics 
as soon as he became interested in the science itself. Thus 
once he was accepted to graduate studies at Boston Univer- 
sity, and had done the first two years of graduate work, he 
started working with Professor Charles Willis in an area in 
the foundations of statistical physics. Willis was interested 
in the problem of deriving rules of statistical mechanics from 
mechanics, and in similar problems. After doing research 
with Willis for some time, Home asked some questions that 
led Willis to believe that his student would benefit from talk- 
ing with the philosopher of physics at Boston University, 
Abner Shimony. And so he sent him to meet him. 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY C© IJJ 

Shimony gave Home the two papers by John Bell, which 
had recently been sent to him by a friend. Abner knew that 
the papers were extremely important, and that they were 
probably being overlooked by the majority of the physics 
community. Realizing that he had in front of him a student 
with a keen mind and a great interest in the foundations of 
quantum theory, Abner handed him the two papers and said: 
"Read these papers and see if we can expand them and pro- 
pose a real experiment to test what Bell is suggesting here." 
Home went home and began to ponder the obscure but deep 
ideas that had escaped the attention of so many physicists. 
What Bell was proposing in his paper was very interesting. 
Bell thought that Einstein's commitment to locality might 
possibly be refuted by experiment (although he seemed to be 
hoping that Einstein's view would win). Was it possible to 
devise an actual experiment that would test whether Ein- 
stein's local realism was right, or whether quantum mechan- 
ics — with its implications of non-locality — was right instead? 
Such an experiment would be of immense value to physics. 

John F. Clauser was born in 1942 in California, where his 
father and uncle as well as other family members had all 
attended and received degrees from Caltech. John's father, 
Francis Clauser, had received a Ph.D. degree in physics from 
Caltech, and at home there were always deep discussions 
about physics. These conversations took place since John 
was in high school, and so he was steeped in the tradition 
of discussions about the meaning and mystery of quantum 
mechanics. His father stressed to John never to simply 
accept what people told him, but rather to look at the 



Ij6 C® ENTANGLEMENT 

experimental data. This principle would guide John 
Clauser's career. 

John went to Caltech, and there, studying physics, he asked 
questions. Clauser was influenced by the teachings of the 
famous American physicist Richard Feynman, who was on 
the faculty at Caltech and about whom stories and legends 
always circulated on campus. John's first rigorous introduc- 
tion to the quantum theory thus took place at Feynman's lec- 
tures, which later were written down and published as the 
famous "Feynman Lectures on Physics." Volume Three of 
these lectures is devoted to the quantum theory, and it is in 
the beginning of this volume that Richard Feynman makes 
his claim that the result of the Young two-slit experiment 
contains the essential mystery, and the only mystery, of quan- 
tum mechanics. 

Clauser caught on quickly to what the key elements in the 
foundations of quantum mechanics were, and some years 
later, when he decided to test Bell's inequality and the EPR 
paradox, he mentioned this desire to his former professor. 
According to Clauser, "Feynman threw me out of his office." 

After Caltech, John Clauser did graduate work in experi- 
mental physics at Columbia University. He was there in the 
late 1960s, working under the supervision of Patrick Tad- 
deus on the microwave background radiation discovery, 
which was later used by cosmologists to support the big bang 
theory. But despite the importance of the problem, Clauser 
was attracted to a different area in physics: the foundations 
of the quantum theory. 

In 1967, Clauser was looking through some obscure 
physics journals at the Goddard Institute for Space Studies 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY C© Ijy 

and noticed a curious article. Its author was John Bell. 
Clauser read the article, and immediately realized something 
that other physicists had not noticed: Bell's article had poten- 
tially immense implications about the foundations of the 
quantum theory. Bell revived the old EPR paradox and 
exposed its essential elements. Furthermore, taken literally, 
Bell's theorem presented a way to experimentally test the 
very essence of quantum mechanics. Since he was familiar 
with the work of David Bohm and his extension of the EPR 
idea in his 1957 work, as well as work by de Broglie, Clauser 
wasn't completely surprised by Bell's theorem. But having 
been raised as a skeptic, Clauser tried to find a flaw in Bell's 
argument. He spent much time looking for a counter-exam- 
ple, trying to refute Bell's remarkable theorem. But after 
spending weeks on the problem Clauser was satisfied that 
there was nothing wrong with the theorem; Bell was right. It 
was now time to make use of the theorem, and to test the 
very foundations of the quantum world. 

Bell's paper was clear to Clauser in every respect save the 
experimental aspects of the predictions of the theory, which 
made the cautious Clauser decide to dig through the physics 
literature looking for experiments that may have been over- 
looked by Bell, and which might shed light on the problem 
addressed by the theorem. The only thing Clauser could find, 
however, was the Wu and Shaknov experiment on positron- 
ium emission (the release of two high-energy photons as a 
result of an electron and a positron annihilating each other) 
from 1949, which did not fully address the correlation prob- 
lem. Bell's paper did not provide a clear way for experimen- 
talists to conduct an experiment along the lines of the paper. 



Ij8 C© ENTANGLEMENT 

Since Bell was clearly a theorist, he assumed — as theorists 
often do — an ideal experimental setup: ideal apparatus that 
does not exist in the lab, and ideal preparation of the corre- 
lated particles. It was time that someone versed both in 
theory and in experimental physics took over from where 
Bell had left off, and designed an actual experiment. 

Clauser went to talk with Madame Wu at Columbia to ask 
her about her own experiments on positronium. As Bohm 
and Aharonov showed in 1957, the two photons produced in 
such a way are entangled. He asked Madame Wu whether 
she had measured the correlations between the photons in 
her experiments. She said that she had not made these mea- 
surements. Had she done so, Clauser thought he could have 
obtained from her the experimental results he needed to test 
Bell's inequality. (Wu could not have made such measure- 
ments because the high-energy photons from positronium 
annihilation do not give enough information about pair-by- 
pair polarization correlation to test Bell's inequality, as 
Home and Shimony, and Clauser, were about to find out 
independently.) Wu sent John to speak with her graduate stu- 
dent Len Kasday, who was redoing her positronium experi- 
ments from decades earlier. Kasday and Wu's new 
experiment (done jointly with J. Ullman) eventually did mea- 
sure these correlations and would be used to test Bell's 
inequality. Its results, published in 1975, would be used to 
add to the evidence in favor of quantum mechanics; although 
in order to measure the correlations, Kasday and Wu had to 
make strong auxiliary assumptions they could not test, weak- 
ening their results. But this would happen years in the future. 
For now, Clauser knew that the Wu and Shaknov results 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY Co Ijp 

were useless in testing Bell's inequality, and he had to develop 
something new. 

All on his own, Clauser kept working, pretty much ignor- 
ing what was supposed to be his dissertation area on 
microwave background radiation. But the reaction of fellow 
physicists was not favorable. It seemed that no one he talked 
to thought that Bell's inequalities were worth pursuing exper- 
imentally. Physicists either thought that such experiments 
could not produce results, or they thought that Bohr had 
already won the debate with Einstein thirty years earlier, and 
that any further attempts to reconcile Einstein's objections 
with Bohr's answers would be a waste of time. But Clauser 
persisted. Going over the results of the old Wu-Shaknov 
experiment, Clauser concluded that something beyond their 
experimental results was needed in order to test quantum 
mechanics against the hidden-variables theories in the way 
Bell's theorem suggested. He kept working on the problem, 
and in 1969 he finally made a breakthrough, as a result of 
which he sent an abstract of a paper to be presented at a 
physics conference, suggesting how an experiment to test 
Bell's inequality might be carried out. Clauser's abstract was 
published in the Bulletin of the Washington meeting of the 
American Physical Society in the spring of 1969. 

Back in Boston, Abner Shimony and Mike Home spent much 
time in late 1968 and early 1969 steadily working to design 
what they thought would be one of the most important 
experiments physicists would ever attempt. Their path was 
very similar to the one taken by Clauser in New York. "The 
first thing I did after I got the commission from Abner was 



l6o & ENTANGLEMENT 

to look at the Wu and Shaknov results," recalled Mike 
Home. Mike understood that the Wu and Shaknov experi- 
ment on positronium annihilation should have had some rel- 
evance to the problem of Bell's theorem because the two 
photons emitted by the electron and positron as they anni- 
hilate each other had to be entangled. The problem was that 
these two photons were of very high energy and, as a result, 
their polarizations were more difficult to measure than those 
of visible light. To expose the polarization correlations, Wu 
and Shaknov had scattered the pairs of photons off electrons 
("Compton scattering"). According to quantum mechanical 
formulas, the correlations between polarization directions of 
the photons are weakly transferred by the Compton effect 
into correlations of the directions in space of the scattered 
particles: that is, up-down or right-left or somewhere in 
between. Mike suspected, as had John Clauser, that this 
transfer is statistically too weak to ever be useful in a Bell 
experiment. To prove this once and for all, Mike constructed 
an explicit mathematical hidden-variables model that fully 
met the EPR locality and reality demands and yet reproduced 
exactly the quantum predictions for the joint Compton 
scattering. 

Thus, the experimental results of Wu and Shaknov — or 
any future refinement of their experiment using Compton 
scattering — could not be used to discriminate between the 
two alternatives: local hidden variables (as suggested by Ein- 
stein) vs. quantum mechanics. Something completely new 
had to be designed. 

Mike showed Abner his explicit local hidden variables 
model, and the two of them decided that visible photons were 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY C© l6l 

needed for the experiment. Polaroid sheets, calcite prisms, 
and some other optical devices exist to analyze the polariza- 
tion direction of visible-light photons. Such a device is shown 
below. 

Sheet of 
pol arized material 




Abner asked a number of experimentalists for advice on 
such experiments, and finally learned from an old Princeton 
classmate, Joseph Snider, then at Harvard, that an optical 
correlation experiment of the required type had already been 
conducted at Berkeley by Carl Kocher and Eugene Commins. 
Abner and Mike soon found out that the Kocher-Commins 
experiment used polarization angles of zero and ninety 
degrees only — so their results could not be used to test Bell's 
inequality, since the intermediate angles were the ones that 
would offer the determination. Technically, in order to con- 
duct the very sensitive test required to determine between the 
two alternatives of Bell's theorem (quantum theory versus 
hidden variables), the experiment had to be carried out at a 
wide array of such angles. This is shown below. 



l6l & ENTANGLEMENT 




Angle 



Hidden Variables 
Quantum Mechanics 



As can be seen from the figure above, the difference 
between quantum theory and hidden-variable theories is sub- 
tle. Only through studying very minutely what happens with 
pairs of photons as the angle between them changes over a 
range of values can a researcher detect which of the two 
theories is correct. Mike and Abner worked on designing the 
actual experiment with all its requirements so that its results 
would determine which of the two alternatives was correct: 
Einstein or quantum mechanics. 

They quickly designed a modification of the Kocher-Com- 
mins experiment that would allow a physicist to test Bell's 
inequality under ideal conditions. All an experimentalist 
would have to do was measure the polarization direction of 
each photon of an entangled pair along appropriate axes, 
different from those used by Kocher and Commins. One 
problem here was the fact that only a few photon pairs 
would obey the idealized condition of emanation at 180 
degrees from each other. So in the next stage, Home and Shi- 
mony relaxed this unrealistic and restrictive assumption and 
allowed for the collection of photon pairs separated by angles 
other than 180 degrees. Doing so, however, required a much 
more complicated calculation to analyze the experimental 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY Co 163 

results. With the help of Richard Holt, a student of Frank 
Pipkin at Harvard University, who was interested in per- 
forming the experiment, Mike Home was able to calculate 
the quantum-mechanical predictions for the polarization cor- 
relations in this realistic case. Interestingly, these calculations 
agreed with those performed two years later by Abner Shi- 
mony using the quantum-mechanical rules for angular 
momentum addition. 

"This was clearly my best paper on physics," recalled Shi- 
mony, when he described to me the paper he and Mike were 
writing on a design for an experiment to test Bell's inequali- 
ties with actual laboratory results in order to see whether 
nature behaved in a way consistent with the existence of local 
hidden variables or in accordance with the rules of quantum 
mechanics. Their proposed experiment would use Bell's mag- 
ical theorem to determine which of two possibilities was true: 
Einstein's assertion that quantum mechanics was an incom- 
plete theory, or Bohr's contention that it was complete. In 
deciding whether the quantum theory was correct, the exper- 
iment would also reveal whether, as Einstein feared, there 
was a possibility of "spooky action at a distance," that is, 
nonlocal entanglement. Unbeknownst to them, their 
thoughts at that time were already entangled with those of 
another physicist, John Clauser, working on the same prob- 
lem only two hundred miles away. 

As part of their preparations, Home and Shimony spoke 
with many experts. "We made a nuisance of ourselves," said 
Shimony. They asked experimentalists about various tech- 
niques that would allow them to test the theorem. They had 
to find an apparatus that would emit pairs of low-energy 



164 C© ENTANGLEMENT 

photons that were entangled with each other, determine a 
way of measuring their polarizations, calculate the quantum- 
mechanical predictions for the correlations of these polar- 
izations, and show that the calculated correlations violated 
Bell's inequality. After many months of work, they finally 
had a design, and the paper was almost complete. They 
hoped to present it at the spring meeting of the American 
Physical Society in Washington, D.C., but missed the dead- 
line for submission. "I thought: What would it matter?" said 
Shimony, "Who else would be working on such obscure 
problems? So we passed up on the conference, and prepared 
to send the paper directly to a journal. Then I got the pro- 
ceedings for the conference, and discovered the bad news: 
Someone else had the very same idea." That person was John 
Clauser. 

Abner called Mike early on a Saturday morning. "We've been 
scooped," he said. The two met the following Monday at the 
physics department at Boston University, and asked the 
advice of other physicists: "What should we do? — someone 
else has done what we have . . . ." Most answered them: 
"Pretend you don't know about it, and just send the paper to 
a journal." That didn't seem right to them. Finally, Abner 
decided to call his own former doctoral adviser at Princeton, 
Nobel laureate Eugene Wigner. "Just call the man," was 
Wigner's suggestion, "talk to him about it." So Abner did. 
He called John Clauser in New York. 

While honest and direct, this approach could have had an 
unpleasant outcome. Scientists tend to be territorial animals, 
jealously protecting their turf. And since Clauser had already 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY (D l6$ 

published the abstract of a paper very similar to the one that 
Home and Shimony had been working on so hard, he might 
not have responded well to the newcomers to the same 
project. 

Many people, when rinding themselves in such a position, 
might say: "This is my research project — you got your idea 
a bit too late!" and hang up the phone. But not John Clauser. 
To Abner and Mike's great surprise, Clauser's response was 
positive. "He was thrilled to hear that we were working on 
the same problem — one that nobody else seemed to care 
about," Mike Home told me, recalling that fateful moment. 

Actually, Shimony and Home had a secret weapon at their 
disposal, which made Clauser even more willing to cooper- 
ate with them. The two of them had already lined up a physi- 
cist who was ready to conduct the experiment in his lab. This 
person was Richard Holt, then at Harvard University. In 
addition to being honestly happy to find two other souls 
interested in the very same arcane area that attracted him, 
Clauser knew they could start the experiment, and he wanted 
to be in on it. Incidentally, Clauser's design of an experiment 
made the same idealization that Home and Shimony had 
originally made — a restriction to photon pairs that are sepa- 
rated by an angle of 180 degrees to each other — and were in 
the process of eliminating in cooperation with Holt. 

Alone, John Clauser would have been left in search of the 
means to conduct the experiment he sought; and here were 
Mike Home, Abner Shimony, and Richard Holt, ready to 
move forward. He didn't have to think a minute. He was in 
on it with them. 

The four of them, Shimony, Home, Clauser, and Holt, 



l66 C® ENTANGLEMENT 

began a very fruitful collaboration on the subject, and within 
a short time produced a groundbreaking paper detailing how 
an improved experiment could be done to give a definitive 
answer to Bell's question: Which answer is right, Einstein's 
local realism, which says that what happens here does not 
affect what happens elsewhere, or quantum mechanics, 
which allows for nonlocal entanglement? 

The Clauser-Horne-Shimony-Holt (CHSH) paper, pub- 
lished in Physical Review Letters in 1969, contained an 
important theoretical improvement over Bell's pioneering 
derivation of his inequality. In addition to the existence of a 
hidden variable that locally determines the outcome of a 
measurement, Bell had assumed a constraint borrowed from 
quantum mechanics: that if the same observable quantity is 
measured in both particles, then the outcomes are strictly 
correlated. Bell's derivation of his inequality made essential 
use of this constraint. Clauser, Home, Shimony, and Holt did 
away with Bell's restrictive assumption, and thus improved 
his inequality. The remainder of the paper proposed an exten- 
sion of the experimental design used by Carl Kocher and 
Eugene Commins at Berkeley, in which two photons were 
produced and the correlation between their polarization 
directions was measured, in a 1966 experiment, without 
knowledge of Bell's theorem. 

Kocher and Commins had used the atomic cascade method 
for producing their correlated photons, and CHSH concurred 
that this was the right method for their own experiment. 
Here an atom is excited and emits two photons as it decays 
two levels down; and the two photons are entangled. The 
source of the photons was a beam of calcium atoms ema- 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY & l6j 

nating from a hot oven. The atoms in the beam were bom- 
barded by strong ultraviolet radiation. As a response to this 
radiation, electrons in the calcium atoms were exited to 
higher levels, and when they descended again, they released 
pairs of correlated photons. Such a process is called an 
atomic cascade because by it an electron cascades down from 
a high level, through an intermediate level, down to a final 
level, releasing a photon at each of the two steps down. 
Because the initial and the final levels are both states of zero 
total angular momentum, and angular momentum is a con- 
served quantity, the emitted photon pair has zero angular 
momentum, and that is a state of high symmetry and strong 
polarization correlation between the photons. The idea of 
such an atomic cascade is demonstrated in the figure below. 

J=0 



551 nm 



423 nm 



-J=1 



-J=0 



A note at the end of the CHSH paper acknowledged that 
the paper presents an expansion of the ideas of John Clauser 
as presented at the spring 1969 meeting of the American 
Physical Society. Thus a situation that was potentially com- 
petitive resulted in a great cooperation, entangling the lives 
of the four physicists. As John Clauser recalled years later: 
"In the process of writing this paper, Abner, Mike, and I 



l68 C© ENTANGLEMENT 

forged a long lasting friendship that was to spawn many sub- 
sequent collaborations." 

After receiving his Ph.D. from Columbia, Clauser moved to 
the University of California at Berkeley to assume a post- 
doctoral position with the famous physicist Charles Townes, 
the Nobel laureate who shared in the invention of the laser. 
Clauser's postdoctoral research project was in the field of 
radio astronomy, but — as before — he had little interest in 
anything but the foundations of quantum mechanics. And 
now, having made the breakthrough into testing Bell's 
inequality, and with the success of his joint CHSH paper, he 
had even less patience for anything else. Clauser was ready to 
perform the actual experiment. The CHSH paper was to be 
the blueprint for this historic experiment. Fortunately for 
John, Gene Commins was still at Berkeley. Clauser thus 
approached Charles Townes and asked him if he would mind 
if he, Clauser, would spend some time away from radio 
astronomy trying to perform the CHSH experiment. To his 
surprise, Townes agreed, and even offered that Clauser spend 
half his time on the project. Gene Commins was also happy 
to cooperate on a project that was based on his own past 
experiment with Kocher, and so he offered Clauser that his 
own graduate student, Stuart Freedman, would help with the 
experiment. Back in Boston, Abner and Mike were rooting 
for him. 

Clauser and Freedman began to prepare the apparatus 
needed for their experiment. Clauser was pushing Freedman 
to work harder and faster. He knew that back at Harvard, 
Richard Holt, his coauthor on CHSH, was preparing his own 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY (D 169 

experiment. Freedman was a 2 5 -year-old graduate student 
with little interest in the foundations of quantum mechanics, 
but he thought that this should be an interesting experiment. 
Clauser was desperate to finish the experiment; he knew that 
Holt and Pipkin at Harvard were moving ahead, and he 
wanted to be the first to test whether the quantum theory 
was valid. Deep down, he was betting against the quantum 
theory, believing that there was a good chance that Einstein's 
hidden variables were correct and that quantum mechanics 
would break down on entanglement of photons. 

Earlier, while he was still working alone on his paper 
designing the experiment, Clauser had written to Bell, Bohm, 
and de Broglie, asking them whether they knew of any sim- 
ilar experiments, and whether they thought such experiments 
would be important. All had replied that they knew of no 
such past experiments and that they thought that Clauser's 
design might be worth pursuing. John Bell was especially 
enthusiastic — this was the first time that anyone had written 
him in response to his paper and his theorem. Bell wrote 
Clauser: 28 

"In view of the general success of quantum mechanics, it 
is very hard for me to doubt the outcome of such experi- 
ments. However, I would prefer these experiments, in which 
the crucial concepts are very directly tested, to have been 
done and the results on record. Moreover, there is always the 
slim chance of an unexpected result, which would shake the 
world!" 

As we will see, there is even a complicated process called 
entanglement swapping, in which two entangled particles 
swap their mates. In a sense, this is what happened to the 



iyO <© ENTANGLEMENT 

people in this grand scientific drama played out across the 
United States in 1969. Shimony and Home got entangled 
with Holt, who was going to conduct an experiment accord- 
ing to their specifications. When they found out about 
Clauser's own work, they used the fact that Holt was going 
to do their experiment. As a result, Clauser got entangled 
with them. The four of them created the seminal CHSH 
paper proposing an important experiment, and Richard Holt 
got dzs-entangled with the others and went on to conduct his 
own experiment. Perhaps this is the reason that in recalling 
the relationships among them many years later, Clauser men- 
tioned only Home and Shimony, but not Holt. 

Work on performing the experiments proceeded. Bell's 
enthusiasm, and the support and cooperation from Clauser's 
new friends in Boston, encouraged Clauser in his quest. 
Would Bell's inequalities be violated, proving the quantum 
theory, or would Einstein and his colleagues be the winners 
and local realism the answer? Clauser, believing in Einstein 
and local realism, made a bet with Yakir Aharonov of the 
Technion in Haifa, Israel, with two-to-one odds against 
quantum theory. Shimony kept an open mind; he would wait 
and see which theory was correct. Home believed that quan- 
tum mechanics would prevail. He relied on the fact that the 
quantum theory had been so successful in the past: it never 
failed to provide extremely accurate predictions in a wide 
variety of situations. 

Clauser and Freedman constructed a source of photons in 
which calcium atoms were excited into high states. Usually, 
when the electron in the calcium atom descends back to its 
normal level, it emits a single photon. But there is a small 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY C© IJI 

probability that two photons would be produced, a green 
one and a violet one. The green and violet photons produced 
in this way are correlated with each other. The experimental 
design used by Clauser and Freedman is shown below. Pho- 
ton pairs produced by the atomic cascade are directed toward 
polarizers Pi and P2, set at different angles, and then the 
photons that pass through the polarizers are detected by a 
pair of detectors, Di and D2, and finally, a coincidence 
counter, CC, records the results. 



^ It) -' \Q ^ 



cc 



The light signal used in the experiment was weak, and 
there were many spurious cascades producing non-correlated 
photons. In fact, for every million pairs of photons, only one 
pair was detected in coincidence. Later, this flaw would be 
called the "detection loophole," and the problem would need 
to be addressed. Because of this low count, it took Clauser 
and Freedman more than two hundred hours of experimen- 
tation to obtain a significant result. But their final result 
strongly supported the quantum theory and countered Ein- 
stein's local realism and hidden variables theories. The 
Clauser-Freedman result was highly statistically significant. 
Quantum mechanics beat hidden variables by over five stan- 



i 7 z 



ENTANGLEMENT 



dard deviations. That is, the measured value of S (the quan- 
tity used in Bell's inequality) agreed with the prediction of 
quantum mechanics and was greater than the limit of 2, 
allowed in the inequality, by five times the standard deviation 
of the experimental data. 

The Clauser-Freedman experiment provided the first defin- 
itive confirmation that quantum mechanics is intrinsically 
non-local. Einstein's realism was dead — quantum mechanics 
did not involve any "hidden variables." The experiment pro- 
vided Freedman with his Ph.D. thesis. Clauser and Freedman 
published the results of their experiment in 1972. The figure 
below shows their results. 




45' 



90' 



135° 180° 225° 

Angle 



270° 315° 



360° 



The Clauser-Freedman experiments left some questions 
unanswered. In particular, the experimental design created a 
large number of unobserved photons, which were produced 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY C© J73 

in order to obtain the entangled pairs. Also, the detectors 
used were of limited efficiency, and the question arose as to 
how these limited efficiencies and large numbers of unob- 
served photons might affect the conclusions. Clauser and 
Freedmen had done a magnificent job — they provided the 
best evidence for quantum mechanics and against hidden 
variable theories. They achieved these results using the best 
available technology, but this technology was not perfect. 
Ironically, while Clauser was a postdoc working for Townes, 
who had invented lasers, Clauser could not use lasers in his 
experiment with Freedman, since it was still not known how 
to do so. Lasers would have helped him and Freedman by 
enabling them to produce entangled pairs of photons more 
quickly. 

Meanwhile, back at Harvard, Holt and Pipkin had also 
obtained results. But these were consistent with Einstein and 
local realism and hidden variables, and against the quantum 
theory. Since both Holt and Pipkin were believers in the 
quantum theory, they decided not to publish their results. 
Instead, they simply waited for the Berkeley team to publish 
its results, and see what they obtained. 

The Holt and Pipkin experiment at Harvard used an iso- 
tope of mercury (mercury 200), which exhibits a similar cas- 
cade when bombarded by a stream of electrons. Holt and 
Pipkin's experiment lasted 150 hours, because their experi- 
ment, too, suffered from many stray photons. Having seen 
the Clauser-Freedman results, Holt and Pipkin decided not to 
go ahead and publish their contrary results in a journal. 
Instead, in 1973, tne y distributed an informal preprint of their 
experimental results to other physicists. Eventually, after oth- 



1J4 Ccs ENTANGLEMENT 

ers had also come out with experimental results supporting 
quantum mechanics, Holt and Pipkin concluded that their 
experiment had suffered from a systematic error of some kind. 

Although he was no longer working in radio astronomy 
with the famous Charles Townes, John Clauser managed to 
stay on at Berkeley as a member of the atomic-beams group 
headed by Howard Shugart. This allowed him to continue his 
work. And Clauser, ever the careful experimentalist, decided 
to revisit his competitors' results and try to replicate them. 
He was puzzled by their contrary results and wanted to find 
out the reason for the disagreement. He made only minor 
modifications of the experimental setup used by Holt and 
Pipkin, and used a different isotope of mercury (mercury 
202) for the atomic cascade. His results, reported in 1976, 
were again in agreement with the quantum theory and 
against local hidden-variable theories. 

The same year, at Texas A & M University, Ed S. Fry and 
Randal C. Thompson carried out an experiment with mer- 
cury 200, but using a greatly improved design. Because Fry 
and Thompson excited their atoms with a laser, their light 
signal was several orders of magnitude more powerful than 
the signals achieved by the experimenters who did similar 
work before them. Fry and Thompson were able to obtain 
their results in only 80 minutes of experimentation. These 
results supported quantum mechanics and argued against the 
hidden-variables hypothesis. 

In 1978 Abner Shimony was at the University of Geneva in 
Switzerland. During that year, Abner and John Clauser wrote 
a joint paper about entanglement, refining their points via 
long-distance telephone, which surveyed all that was known 
thus far about the bizarre phenomenon. The article discussed 



THE DREAM OF CLAUSER, HORNE, AND SHIMONY C© IJJ 

in depth all the experimental findings about entanglement 
that had been achieved until that year and established that 
the phenomenon is real. In addition to the experiments men- 
tioned earlier, there were results on Bell's theorem by three 
other teams that conducted experiments in the 1970s. 

One was a group led by G. Faraci, of the University of 
Catania in Italy. This group, which published in 1974, used 
high-energy photons (gamma rays) from positronium anni- 
hilation (when an electron and a positron annihilate each 
other). Both Horne-Shimony and Clauser had decided not to 
do a Bell experiment with photon pairs from positronium 
annihilation, but the Catania group was able to use data 
from this kind of experiment by making an additional tech- 
nical assumption similar to the one made by Kasday, Ullman, 
and Wu. Doubts about this assumption are responsible for 
the relative neglect of these experimental results. 

Another group, comprised of Kasday, Ullman, and Wu, of 
Columbia University, which published in 1975, a l so use d 
positronium annihilation photons. And in 1976, M. Lamehi- 
Rachti and W. Mittig, of the Saclay Nuclear Research Cen- 
ter, used correlated pairs of protons in the singlet state. The 
results of these groups agreed with the quantum theory and 
countered the hidden-variables alternative. 

Following the successes in proving the validity of the quan- 
tum theory, other theoretical arguments were improved as 
well. This is usual in science: when the theory advances, the 
experiments aren't far behind, and when experiments advance, 
the theory that explains them follows. When one moves for- 
ward, the other is not far behind, and once it catches up, it 
reinforces its symbiote. Bell, Clauser and Home strengthened 
the theoretical arguments for testing Einstein's local reality. 



Ij6 C® ENTANGLEMENT 

They proved a testable inequality, using the assumption of a 
stochastic (probability-governed) rather than deterministic hid- 
den variables theory. These parallel advances in fundamental 
physics, all revolving around his remarkable theorem, drew 
John Bell into the discussion. Clauser, Home, and Shimony 
embarked on a years-long exchange of ideas with John Bell. 

While all but one of the experiments carried out in the 
1970s provided good confirmation of the validity of the 
quantum theory, it would remain for another scientist, on 
the other side of the globe, to provide an even better test of 
Bell's inequality using both laser technology and a greatly 
improved design that would close an important loophole and 
thus provide a more complete proof of the mysterious non- 
local nature of the universe. 

In order to really test Einstein's assertion against quantum 
mechanics, a scientist would also need to account for the pos- 
sibility — remote and outrageous as it may seem — that, some- 
how, signals may be exchanged between the polarization 
analyzers at opposite ends of the laboratory. This problem 
would be addressed by Alain Aspect. 

Abner had a dream that he heard a lecture by Alain Aspect, 
in which Aspect asked whether there is an algorithm — a 
mechanical decision procedure — for deciding whether a given 
state of two particles is entangled or not. Abner passed this 
question on to Wayne Myrvold, an expert on computability 
in quantum mechanics, who had just had his doctoral thesis 
accepted by the philosophy department at Boston University. 
Within two weeks, Myrvold solved the problem. His answer 
to Aspect's question in Shimony's dream was that no such 
algorithm is mathematically possible. 



15 

Alain Aspect 



"Bohr had an intuitive feeling that Einstein's position, 
taken seriously, would conflict with quantum mechanics. 
But it was Bell's theorem that materialized this contradic- 
tion." 

— Alain Aspect 



^lain Aspect was born in 1947 in a small village in 
/ 1 southwestern France, not far from Bordeaux and 
JL JL Perigord, a region in which good food and excellent 
wines are an integral part of the culture. To this day, Aspect 
makes his own pate and keeps his heart healthy by drinking 
the region's famous red wines. Alain views himself as living 
proof of what has come to be known as "the French para- 
dox": the fact that the French can eat heavy foods and yet 
enjoy good cardiovascular health by regularly drinking red 
wine. 

Since early childhood, Alain has been interested in science, 
especially physics and astronomy. He loved looking at the 
stars, and he read Jules Vernes's books, especially enjoying 
Twenty Thousand Leagues Under the Sea. He always knew 
he would become a scientist. 



177 



Ij8 C© ENTANGLEMENT 

Alain moved to the nearest town to go to school, and after 
finishing high school he moved to yet a bigger city, Bordeaux, 
to prepare for the admissions examinations to France's best 
schools, the renowned Grandes Ecoles. He succeeded in pass- 
ing the examinations and moved to the greatest city of all 
and the intellectual and academic heart of all Europe: Paris. 
At the age of 24, Aspect received the graduate degree he calls 
"my small doctorate," and before continuing to study for his 
"big doctorate," he took a few years off and volunteered to 
do social service in Africa. Thus in 1971 he flew to 
Cameroon. 

For three years, under the scorching African sun, Alain 
Aspect worked hard helping people live better under adverse 
conditions. But he spent all his spare time reading and study- 
ing one of the most complete and deep quantum theory 
textbooks ever written: Quantum Mechanics, by Cohen- 
Tannoudji, Diu, and Laloe. Alain immersed himself in the 
study of the bizarre physics of the very small. While working 
on his degree, he had studied quantum mechanics, but never 
quite understood the physics, since the courses he took 
emphasized only the mathematics of differential equations 
and other mathematical machinery used in advanced physics. 
Here, in the heart of Africa, the physical concepts themselves 
were becoming a reality for the young scientist. Aspect began 
to understand some of the quantum magic that permeates 
the world of the very small. But of all the strange aspects of 
the quantum theory, one caught his attention more than all 
the rest. It was the decades-old proposal by Einstein, Podol- 
sky, and Rosen that was taking on a special meaning to him. 

Aspect read the paper by John Bell, then an obscure physi- 



ALAIN ASPECT C© 1J<) 

cist working at the European Center for Nuclear Research 
(CERN) in Geneva. And the paper had a profound effect on 
Aspect, making him decide to devote all his efforts to study- 
ing the unexpected implications of Bell's curious theorem. 
This would lead him down the path to exploring the deepest 
mysteries of nature. In this, Alain Aspect is similar to Abner 
Shimony. Both men have a deep — even natural and intu- 
itive — grasp of quantum theory. Each one of them, across 
the Atlantic from each other, somehow possesses an ability, 
shared with the late John Bell, of understanding truths that 
had eluded Albert Einstein. 

Like Shimony, Alain Aspect always goes to the origin of a 
concept or an issue. If he wanted to understand entangle- 
ment, Aspect read Schrodinger directly — not an analysis pro- 
posed by some later physicists. And if he wanted to 
understand Einstein's objections to the nascent quantum 
theory, he searched for and read Einstein's own original 
papers of the 1920s and 1930s. But surprisingly, beyond the 
fact that Shimony had a dream in which he saw Aspect make 
a presentation, leading Shimony to develop an important 
question, the two men's lives are not entangled. They move 
in mostly separate circles. While Abner Shimony is an enthu- 
siast, one whose enthusiasm for physics tends to spread to 
those around him — Home, Clauser, Greenberger, Zeilinger — 
spurring them on to greater achievement and discovery, 
Aspect works differently. 

Upon his return from Africa, Alain Aspect devoted himself 
to a thorough study of quantum theory in his native land. 
And in fact France was — and still is — an important world 
center for physics. He found himself in the midst of an elite 



180 C® ENTANGLEMENT 



group of established physicists, from whom he could learn 
much, and on whom he could test his ideas. The names of the 
faculty members listed on his dissertation committee read 
like a Who's Who of French science: A. Marechal, Nobel lau- 
reate C. Cohen-Tannoudji, B. D'Espagnat, C. Imbert, F. 
Laloe. The only non-French member on the committee was 
none other than John Bell himself. 

Like Shimony across the Atlantic, Aspect understood Bell's 
theorem better than most physicists. He was quick to realize 
the challenge that Bell's remarkable theorem issued to physics 
and to Einstein's understanding of science. From Aspect's 
point of view, the essence of the argument between Bohr and 
Einstein was Einstein's conviction that: 

"We must abandon one of the following two assertions: 
1. The statistical description of the wave function is com- 
plete; or: 2. The real states of two spatially separated objects 
are independent from one another." 29 

Aspect understood very quickly that it was this assertion 
by Einstein, as articulated in the EPR paper of 1935, which 
John Bell's theorem addressed so succinctly and elegantly. 
Using the EPR setup, Bell offered an actual framework for 
testing the hypothesis that the quantum theory was incom- 
plete versus the assertion that it was, indeed, complete but 
included distinctly non-local elements. 

Bell's theorem concerns a very general class of local 
theories with hidden, or supplementary, parameters. The 
assumption is as follows: suppose that the quantum theory is 
incomplete but that Einstein's ideas about locality are pre- 
served. We thus assume that there must be a way to com- 
plete the quantum description of the world, while preserving 



ALAIN ASPECT C© l8l 

Einstein's requirement that what holds true here cannot 
affect what holds true there, unless a signal can be sent from 
here to there (and such a signal, by Einstein s own special 
theory of relativity, could not travel faster than light). In such 
a situation, making the theory complete means discovering 
the hidden variables, and describing these variables that 
make the particles or photons behave in a certain way. Ein- 
stein had conjectured that correlations between distant par- 
ticles are due to the fact that their common preparation 
endowed them with hidden variables that act locally. These 
hidden variables are like instruction sheets; and the particles' 
following the instructions, with no direct correlations 
between the particles, ensures that their behavior is corre- 
lated. If the universe is local in its nature (that is, there is no 
possibility for super-luminal communication or effect, i.e., 
the world is as Einstein viewed it) then the information that 
is needed to complete the quantum theory must be conveyed 
through some pre-programmed hidden variables. 

John Bell had demonstrated that any such hidden-variable 
theory would not be able to reproduce all of the predictions 
of quantum mechanics, in particular the ones related to the 
entanglement in Bohm's version of EPR. The conflict 
between a complete quantum theory and a local hidden vari- 
ables universe is brought to a clash through Bell's inequality. 

Alain Aspect understood a key point. He knew that the 
quantum theory had by this time enjoyed a tremendous suc- 
cess as a predictive tool in science. He thus felt that the 
apparent conflict described above and inherent in Bell's the- 
orem and its attendant inequalities could be used, on the con- 
trary, to defeat all local hidden-variables theories. Thus, 



l8l & ENTANGLEMENT 

unlike John Clauser, who before his experiment bet that the 
quantum theory would be defeated and that locality would 
win the day, Aspect set out to design his own experiments 
believing that the quantum theory would be victorious and 
that locality would be defeated. If his contemplated experi- 
ments should succeed, he mused, non-locality would be 
established as a real phenomenon in the quantum world, and 
the quantum theory would repel the attack upon its com- 
pleteness. It is important to note, however, that whatever 
proclivities Clauser and Aspect may have had concerning the 
expected outcomes of their respective experiments, each 
designed an experiment to allow nature to speak without any 
preexisting bias one way or the other. 

Aspect was well aware that Bell's theorem, virtually 
ignored when it first appeared in the mid-1960s, had become 
a tool for probing the foundations of the quantum theory. In 
particular, he knew about Clauser's experiments in Califor- 
nia and the involvement of Shimony and Home in Boston. 
He was also aware of several inconclusive experiments. 
Aspect realized, as he later stated in his dissertation and sub- 
sequent papers, that the experimental setup used by the 
physicists whose work came before his was difficult to use. 
Any imperfection in experimental design had the tendency 
to destroy the delicate structure that would have brought 
about the desired conflict between Bell's inequalities and 
quantum predictions. 

The experimenters were looking for outcomes that were 
very hard to produce. The reason for this was that entangle- 
ment is a difficult condition to produce, to maintain, and to 
measure effectively. And in order to prove a violation of Bell's 



ALAIN ASPECT © 183 

inequality, which would prove quantum predictions, the 
experimental design had to be constructed very carefully. 
Aspect's aim was to produce a superior experimental setup, 
which would allow him, he hoped, to reproduce Bohm's ver- 
sion of the EPR thought experiment as closely as possible, 
and allow him to measure the correlations in his data for 
which quantum mechanics predicts a violation of Bell's 
inequalities. 

Aspect set to work. He built every piece of equipment on 
his own, working in the basement of the Center for Optical 
Research of the University of Paris, where he'd been given 
access to experimental space and apparatus. He built his 
source of correlated photons, and constructed the arrange- 
ment of mirrors, polarization analyzers, and detectors. 
Aspect considered carefully the thought experiment of EPR. 
In the version proposed by David Bohm, the phenomenon in 
question is simpler and Bell's theorem applies: the spins or 
polarizations of two particles are correlated. In contrast, Ein- 
stein's momentum and position framework are more com- 
plicated because these two quantities have a continuum of 
values and Bell's theorem is not directly applicable. After 
thinking about the problem for a long time, Alain Aspect 
reached the conclusion that the best way to test the EPR 
conundrum would be with the use of optical photons, as had 
been done in the best earlier experiments. 

The idea, previously followed by Clauser and Freedman 
as well as their colleagues in Boston Shimony, Home, and 
Holt, was to measure the polarization of photons emitted in 
correlated pairs. Aspect knew that a number of experiments 
of this kind had been carried out in the United States between 



184 C® ENTANGLEMENT 

1972 and 1976. The most recent of these experiments lead- 
ing to results in support of quantum mechanics, conducted 
by Fry and Thompson, was carried out using a laser to excite 
the atoms. 

Aspect decided to carry out a series of three main experi- 
ments. The first was a single-channel design aimed at repli- 
cating the results of his predecessors in a much more precise 
and convincing way. He would use the same radiative cas- 
cade of calcium, in which excited atoms emit photons in cor- 
related pairs. Then, he would conduct an experiment with 
two channels, as had been proposed by Clauser and Home 
to get closer to an ideal experiment. If there is only one chan- 
nel, then the photons that do not enter it may behave as they 
do for one of two reasons: either they hit the polarization 
analyzer but have the wrong polarization to pass through, or 
they miss the entrance of the analyzer. With two channels, 
one can restrict attention to the particles that are detected — 
all of these must have hit the entrance aperture and exited 
through one channel or the other. Such a methodology helps 
close the detection loophole. Finally, Aspect would conduct 
an experiment that was suggested by Bohm and Aharonov in 
1957 and articulated by John Bell. Here, the direction of 
polarization of the analyzers would be set after the photons 
had left their source and are in flight. This is a type of design 
in which experimenters play devil's advocates. In a sense, the 
experimenter is saying: "What if one photon or its analyzer 
sends a message to the other photon or its analyzer, inform- 
ing the other station of the orientation of the analyzer, so 
that the second photon can adjust itself accordingly?" To 
prevent such an exchange of information, the experimenter 



ALAIN ASPECT 



i8 5 



chooses the orientation to be used in the design both ran- 
domly and with delay. Thus, what Alain Aspect was after, 
was a more definitive test of Bell's inequality — a test whose 
results could not be doubted by someone who thinks that 
the analyzers or photons communicate with each other in 
order to fool the experimenter. It should be noted that, in the 
thinking of physicists, communication may not be such a 
bizarre notion, and the intent to fool the experimenter is 
absent from such thinking. What the physicists are worried 
about is the fact that in a physical system that has had a 
chance to reach some equilibrium level, communication by 
light or heat may transfer effects from one part of the system 
to another. 

In the actual experiment, Aspect had to resort to a signal 
that was periodic, rather than perfectly random — however, 
the signal was sent to the analyzers after the photons were in 
flight. This is the essentially new and important element of his 
experiments. 

Aspect's two-channel, but non-switched arrangement 
(reprinted by permission from his dissertation) is shown 
below. 

I II 





\ - 



6- 



Since Alain knew that Bell's inequality had previously been 
used to determine which of the two alternatives, quantum 
mechanics or local realism, was true, he went to Geneva to 
visit John Bell. He told him that he was planning an experi- 



l86 Cs ENTANGLEMENT 

ment that would incorporate a dynamic principle of time- 
varying polarizers to test for Einstein separability, as Bell 
himself had suggested in his paper. Bell looked at him and 
asked: "Are you tenured?" to which Aspect responded by 
saying he was only a graduate student. Bell stared at him 
with amazement. "You must be a very courageous graduate 
student ..." he muttered. 

Aspect began his experiments, and used an atomic beam of 
calcium as his source of correlated photons. The atoms were 
excited by a laser. This caused an electron in each atom to 
move up two levels of energy from its ground state (as was 
done in previous experiments). When the electron descended 
two levels down, it sometimes emitted a pair of correlated 
photons. The energy levels and the entangled photons pro- 
duced by this method of atomic cascade are shown below. 



4s 4p 1 ^ 



The coincidence rate for the experiment, the rate at which 
correlated pairs were indeed detected and measured, was sev- 
eral orders of magnitude higher than the rate obtained by 
Aspect's predecessors. These experiments with a single-chan- 
nel polarizer led to excellent results: Bell's inequality was vio- 
lated by nine standard deviations. This means that quantum 
theory prevailed, no hidden-variables were found to be pos- 
sible, and nonlocality was inferred to exist for these entan- 



ALAIN ASPECT C© l8j 

gled photons — they respond instantaneously to one 
another — with an immensely small probability that these 
conclusions are wrong. This result was very powerful. Next, 
Aspect carried out his two-channel experiments. 

When a photon is blocked by the polarizer in a single- 
channel design, that photon is lost and there is no way to 
determine whether it was correlated with another one and 
how. This is why two-channels were used. What happens 
here is that if a photon is blocked by the polarizer then it is 
reflected by it and can still be measured. This increases the 
coincidence rate of the overall test and makes the experiment 
much more precise. With this greatly improved scheme of 
measurement, the results obtained by Aspect were even more 
precise and convincing. Bell's inequality was violated by 
more than 40 standard deviations. The evidence in favor of 
quantum mechanics and non-locality was overwhelming and 
went far beyond anyone's expectations. 

Then came the ultimate test of non-locality, a test of 
whether a photon could still send a signal to another, versus 
the quantum-mechanical alternative that non-locality pre- 
vails and that the photons — without being able to send sig- 
nals to one another — react to each other's situation 
instantaneously. Aspect designed polarizers whose direction 
in space could be changed at such high speed that the change 
is made while the two photons are in flight. This was 
achieved in the following way. On each side of the experi- 
ment, there were two polarization analyzers, using different 
orientations. Both were connected to a switch that could 
rapidly determine to which of the two analyzers to send each 
photon, and thus which of two possible orientations the pho- 



ENTANGLEMENT 



ton would encounter. This innovation, in fact, was the great- 
est of the Aspect experiments, and the one that was widely 
viewed as the ultimate test of non-locality. 

Aspect's third set of experiments, with switching between 
analyzers while the pairs of photons were in flight, is shown 
in the figure below. 



I (a) 



HpmTk|- 



C1 



x 



/-* 



•/ 






1 



— (§)—*■ 

L 



COINCIDENCES 



n(b) 



C2 



-||»[PM2T- 



\f% 



In explaining the design of his third set of experiments, 
Aspect quoted an important statement by John Bell: "The 
settings of the instruments are made sufficiently in advance 
to allow them to reach some mutual rapport by exchange of 
signals with velocity less than or equal to that of light." In 
such a case, the result at polarizer I could depend on the ori- 
entation, ft, of the remote polarizer II, and vice versa. In this 
case, the locality condition would not hold and could not be 
tested." The scientists are being very careful here. They play 
devil's advocate, allowing for the possibility that the polar- 
izers and the photons interact with each other and provide 
results consistent with local reality. At any rate, when the 
polarizers in the experiment are fixed, the locality condition 
is not enforced and so — in the strictest sense — it is not pos- 



ALAIN ASPECT C© 189 

sible to test the EPR idea, which demands local realism, 
against the quantum theory using Bell's theorem. 

In Aspect's lab, each of the polarizers was placed at a dis- 
tance of 6.5 meters from the source. The total distance 
between the two polarizers as shown in the diagram above 
was 13 meters. So, in order to solve the problem and allow 
for an objective test of "Einstein causality," meaning a test in 
which the photons and polarizers can't "cheat the experi- 
menter" by sending signals to one another, Aspect had to 
design an experimental way of switching polarizer I between 
the settings a and cf and polarizer II between its two settings 
of b and b' in an interval of time that was less than 13 meters 
divided by the speed of light (about 300,000,000 meters per 
second), which is about 4.3X10" 8 seconds (43 nanoseconds). 
Aspect was able to achieve this goal and to build a device 
able to respond at such incredible speeds. 

In the experimental setup shown in the diagram of Aspect's 
experiment, the switching is achieved in less than 43 nanosec- 
onds. The switching is done by an acousto-optical device in 
which light interacts with an ultrasonic standing wave in 
water. When the wave changes in the transparent water con- 
tainer, the beam of light hitting the water is deflected from 
one setting to another. In fact, the switching took place at 
intervals of 6.y and 13.3 nanoseconds, well below the max- 
imum of 43 nanoseconds. 

Aspect's third set of experiments was also successful, and 
again locality and hidden-variables were defeated in favor of 
quantum mechanics. Aspect noted that he would have liked 
to have an experimental setup in which not only the settings 
are changed while the photons are in flight, but also in which 



iyo 



ENTANGLEMENT 



the switching is done purely at random. His design did not 
provide for randomness, but rather a cyclical change of set- 
tings. So, as Anton Zeilinger has pointed out, an extremely 
clever group of photons and polarizers could — in principle — 
"learn" the pattern and try to fool the experimenter. This, of 
course, would be extremely unlikely. Still, Aspect's third set 
of experiments contained an immensely important dynamic 
component, which added to the power of his entire set of 
positive results for quantum mechanics and helped establish 
non-local entanglement as a real phenomenon. 

The figure below shows, as shaded area, the region in 
which Einstein's locality fails in the experiments. 
S 



Angle 




In the following years, still working at the Center of Optics 
at the University of Paris in Orsay, Aspect went on to conduct 
other important experiments in quantum physics. Recalling 
his groundbreaking entanglement experiments of the 1980s, 
he said: "I am also proud of the fact that, besides doing the 
experiments, my work also called attention to Bell's theo- 
rem. At the time I did the work, this wasn't a popular field." 



i6 



Laser Guns 



" [Interference occurs because] one photon must have come 
from one source and one from the other, but we cannot tell 
which came from which." 

— Leonard Mandel 



V lollowing the tremendous success of the Aspect exper- 
#"^iments, which demonstrated definitively (to most 
JL physicists' minds) the reality of entanglement, the 
study of the phenomenon progressed. While Alain Aspect 
and his colleagues at Orsay, as well as researchers who had 
done earlier experiments, used the atomic cascade method 
for producing entangled states, right after these experiments 
were concluded, in the early 1980s, experimental physicists 
began to use a new method. This method, which is still the 
preferred technique for producing entangled photons today, 
is called spontaneous parametric down- conversion (SPDC 
for short). 

Imagine that there is a transparent crystal sitting on a table, 
and that someone shines a light on this crystal. At first, you 
only see the light that comes through the crystal, shining out 



191 



K)2 & ENTANGLEMENT 

the other side. But as the intensity of the light is increased, 
suddenly you see an additional effect: a pale halo that sur- 
rounds the crystal. When you look closer, you notice that the 
faint halo is shimmering with all the colors of the rainbow. 
This beautiful phenomenon is produced by an interesting 
physical effect. It turns out that, while most of the light that 
is shone on the crystal passes through it to the other side, a 
very small percentage of the light entering the crystal does not 
go straight through. This minority of photons undergoes a 
bizarre transformation: each photon that does not go straight 
through the crystal "breaks down" into two photons. Each 
such photon somehow interacts with the crystal lattice, in a 
way that is not completely understood by science, and this 
interaction gives rise to a pair of photons. When the photon 
undergoes this transformation, the sum of the frequencies of 
the two resulting photons is equal to the frequency of the 
original photon. The photons in a pair produced in this way 
are entangled. 

In the down-conversion method of producing entangled 
photons, scientists use a laser to "pump" the crystal with 
light. The crystals used for this purpose are special ones that 
exhibit this property of generating photon pairs. Among the 
crystals that can be used are lithium iodate and barium 
borate. Such crystals are known as non-linear crystals. That 
is because when the crystal lattice atoms are excited, the 
resulting energy that comes out of the lattice is described by 
an equation which includes a non-linear (squared) term. The 
down-conversion method has been used by physicists since 
1970. That year, D. C. Burnham and D. L. Weinberg dis- 
covered the phenomenon when they examined the nature of 



LASER GUNS Ca> J93 

secondary light produced when intense laser light passed 
through a nonlinear crystal, and the crystal seemed suddenly 
bathed in a weak rainbow of colors. The scientists discovered 
that most of the light passed through the crystal, but that 
about one in a hundred-billion photons gave rise to two pho- 
tons. Because the two resulting photons had frequencies 
adding up to that of the original single photon (meaning each 
of them has been bumped down in frequency), physicists 
named the process down- conversion. A single photon was 
converted downward in its frequency to the lower frequen- 
cies of the two resulting photons. But the researchers did not 
realize that the two photons thus produced were in fact 
entangled, and that they had just discovered a valuable way 
of producing entangled photons. These photon pairs are not 
only entangled in their polarization, but also in their direc- 
tion, which is useful for studies involving two-photon 
interference. 

Scientists experimenting with entanglement using the older, 
atomic cascade method had noticed that there was a collec- 
tion efficiency loophole. This effect is due to atomic recoil. 
When the atoms recoil, some of the momentum is lost from 
consideration. Thus the angles made by the resulting entan- 
gled photons were not precisely known, making it difficult to 
identify by direction which photon is associated with another 
in an entangled pair. The down-conversion method is much 
more precise. It is illustrated in the figure below. 



194 & ENTANGLEMENT 



Laser 


Laser beam 
(photons) 


Nonlinear 
Crystal 


^^ 


,v !- 


Correlated photons in 
the two exiting beams 


/\ 


^^ 



The first scientist to make use of the down-conversion 
method to study entanglement was Leonard Mandel. Man- 
del was born in Berlin in 1927, but moved with his family to 
England while he was a young child. He received a Ph.D. in 
physics from the University of London in 1951, and became 
a senior lecturer in physics at Imperial College, the University 
of London, where he taught until 1964. That year, Mandel 
was invited to join the physics faculty at the University of 
Rochester, in New York. In America, Mandel did work on 
cosmic rays, which entailed climbing to the tops of high 
mountains with experimental apparatus that could detect 
and measure these high-energy particles as they passed 
through Earth's atmosphere. At high altitude there were 
many more such particles that could be measured than at 
lower levels. After a number of years of this research, Man- 
del became fascinated with optics as well as with the quan- 
tum theory, which governs the behavior of the particles he 
had been studying. 

In the late 1970s, Leonard Mandel embarked on a series of 
experiments, some with H. Jeff Kimble, demonstrating quan- 
tum effects with laser light. Some of these experiments 
bounced photons off individual sodium atoms. Some of the 
experiments dealt with complementarity: the wave-particle 
duality of light and the quantum-mechanical idea that one of 
these aspects of light, but not both, can be evidenced through 



LASER GUNS Ca> K)J 

any single experiment. Mandel's experiments demonstrated 
some of the most striking quantum properties of light. In 
some experiments, Mandel has shown that if the experi- 
mental design merely allowed the experimenter the possibil- 
ity of measurement, that was enough to change the outcome 
of the experiment from a wave-pattern to particle-like 
behavior. 

In the 1980s, Leonard Mandel and his colleagues began 
to use the parametric down-conversion technique to produce 
entangled photons. One of these experiments, whose results 
were published in 1987 in a paper by R. Ghosh and L. Man- 
del in the journal Physical Review Letters (vol. 59, 1903-5), 
demonstrated an interesting fact about entanglement. The 
Ghosh and Mandel experimental design is shown on the next 
page. 



196 Cs ENTANGLEMENT 



Aperture 




Aperture 



Detector 



Detecting 
Screen 



Aperture 




Aperture 



Detecting 
Screen 



In the experiment above, a nonlinear crystal is pumped by 
a laser, producing pairs of entangled photons. Since the pho- 
ton that enters the crystal can produce a pair of photons in 
any of infinitely many ways (because all that's required is 
that the sum of the frequencies of the progeny be equal to the 
frequency of the parent photon), within a certain range of 
distance on the screen there can be found photons that are 
entangled with each other. 

In the experiment shown in the upper diagram, a single, 
tiny detector is moved along the screen. Ghosh and Mandel 
found, surprisingly, that no interference is present. Hence a 



LASER GUNS Ca> I<)J 

single photon does not exhibit the interference pattern that 
one would expect based on the old Young double-slit exper- 
iment. In the second experiment, shown on the bottom part 
of the figure above, two detectors are used, at separate points 
on the screen. Again, when each detector was moved along 
the screen, no interference pattern was exhibited. Ghosh and 
Mandel then hooked the two detectors to a coincidence 
counter: a counter that registers a count only if both detectors 
fire together. Now, when they fixed one of the detectors and 
moved the other one along the screen, they found that the 
coincidence counter registered a clear interference pattern sim- 
ilar to the one shown in the Young double-slit experiment. 

The reason for this surprising finding is that, while in quan- 
tum theory a single photon is shown to travel both paths and 
to interfere with itself, as exhibited by the Young experiment, 
with entangled photons the situation is different. An entan- 
gled pair of photons constitutes a single entity even while 
they are separate from each other. What happens here is that 
the entangled two-photon entity is in a superposition of two 
product states, and thus is the entity that interferes with itself. 
This is why the interference pattern appears only when we 
know what happens simultaneously at two locations on the 
screen — that is, when we track the two entangled photons 
as a single entity — and only in this framework do we find the 
familiar peaks and valleys of intensity interference, for a pair 
of photons seen as one element. Here, two distant observers, 
one placed at each detector, must compare their data in order 
to see that something is happening — each observer alone sees 
only a random arrival of photons, with no pattern, and with 
constant average count rate. This finding demonstrates an 



I<)8 C© ENTANGLEMENT 

important idea about entanglement: that it is not correct to 
think of entangled particles as separate entities. In some 
respects, entangled particles do not have their own individ- 
ual properties but behave as a single entity. 

Another kind of experiment was proposed in 1989 by 
James Franson of Johns Hopkins University. He pointed out 
that two-particle interference fringes can arise when we don't 
know when the two particles were produced. Raymond 
Chiao of the University of California at Berkeley and his col- 
leagues have performed an experiment based on Franson's 
design, and so have Mandel and his colleagues. This kind of 
experimental arrangement uses a short and a long path in 
each of two arms, separated by half-silvered mirrors. Which 
route did each photon take? The entangled photons in the 
down conversion are produced at the same time, and arrive 
together. But since we don't know when they were produced, 
we have a superposition of the long path for both photons 
and the short path for both photons. This produces a tem- 
poral double-slit arrangement. 

Another physicist to make extensive use of the SPDC tech- 
nique to produce entangled photons was Yanhua Shih of the 
University of Maryland, who in 1983 began a series of exper- 
iments aimed at testing Bell's inequality. His experiments 
were very precise and led to results in good agreement with 
quantum mechanics and in violation of Bell's inequality. Shih 
and his colleagues were able to demonstrate a violation of the 
Bell inequality to an extent of several hundred standard devi- 
ations. These results were statistically very significant. Shih's 
team conducted experiments with delayed-choice setups as 



LASER GUNS & 199 

well, and here, too, they were able to confirm the agreement 
with quantum mechanics to very high accuracy. 

Shih then studied the effects of a perplexing phenomenon 
called the quantum eraser. When we can tell, using detectors 
in an experiment, which of two paths were taken by a pho- 
ton, no interference pattern appears. Thus, in a "which- 
path" design, we observe the particle-like nature of light. If 
the experimental design is such that the experimenter cannot 
tell which of two paths were taken by a photon, we are in 
the quantum "both-paths" design. In this case, the photon 
is viewed as taking both paths simultaneously. Here, an 
interference pattern can appear and the experiment thus 
exhibits the wave-nature of light. Recall that by Bohr's prin- 
ciple of complementarity, it is impossible to observe in the 
same experiment both the wave- and the particle-nature of 
light. 

Shih and his colleagues constructed strange experiments 
that can "erase" information. Even more stunningly, they 
used a delayed-choice eraser. Here, an entangled photon pair 
was produced and injected into a complex system of beam- 
splitters (half-silvered mirrors that reflect a photon or pass it 
through with probability one-half). After one photon was 
already registered, in terms of its position on a screen, the 
setup was switched randomly such that some of the time the 
experimenter could tell which path was taken and some of 
the time not. Thus it could be determined after the first pho- 
ton hit the screen whether it had wave or particle nature 
when it hit the screen based on what was a fraction of a sec- 
ond later encountered by its twin that was still in flight. 

But the most interesting experiment Shih and his colleagues 



200 



ENTANGLEMENT 



have performed from the point of view of this book, and also 
with an eye toward applications in technology, was the Ghost 
Image Experiment. This experiment used one member of 
each pair of entangled photons to make the other, distant 
member of the same pair help create a "ghost" image at the 
distant location. 30 The diagram of this experiment is shown 
below. 



Laser 
pump 



BBOI 



Prism 



X 



D '£ 



.Collection lens 



-Aperture 



Filter 



Gating 




Lens 




Filter. 



Polarizing Idler 
beam 
splitter 



-?TH* 



X-Y Scanner 
fiber 



As we see from the figure, a laser pumps a nonlinear crys- 
tal (barium borate), producing the SPDC entangled photons, 
which then go through a prism and on to a beam splitter that 
splits them based on their polarization direction. Thus, one 
of each pair of entangled photons goes up, through a lens, 
and encounters a filter with an aperture. The aperture is in 
the form of the letters UMBC (for University of Maryland, 
Baltimore County — Shih's university). Some of the photons 
are blocked, but the ones that go through the letter-apertures 



LASER GUNS <© 201 

are then collected by a lens and detected by a detector. The 
first detector is linked to a coincidence counter along with the 
second — which is collecting the twin photons that go through 
the filter. These twins went straight through the beam split- 
ter. They hit a filter and a scanning fiber that records their 
locations on the screen. Only those in coincidence with the 
twins that went through the UMBC apertures are recorded. 
They form the ghost image of UMBC on the screen. This 
ghost image is shown below. 



3.5 mm 



I UMBC 




Thus, using entangled photons, the image UMBC was 
transported to a distant location by twins of photons that 
went through the letters, providing a dramatic demonstra- 
tion of an interesting aspect of entanglement. The image is 
transformed to create the ghost using two elements. First, we 
have the photons arriving at the screen with the scanning 
fiber: but not all arriving photons are counted. We commu- 
nicate with whoever is observing the twins, the photons 



202 C® ENTANGLEMENT 



entangled with the photons arriving at the screen, by using 
the coincidence counter. We only count screen photons that 
"double click" with a twin that has passed through the let- 
ter-aperture. It is this combination of entanglement with a 
"classical channel" of information that allows us to create 
the ghost image. 

The next stage in Yanhua Shih's career took him to the 
most exciting project of all: quantum teleportation. Some 
basic ideas about teleportation have analogous twins in the 
ideas of the ghost experiment. In particular, quantum tele- 
portation entails the use of two channels simultaneously: an 
"EPR channel," meaning a channel of the "action-at-a-dis- 
tance" of entanglement (which is immediate); and a "classi- 
cal channel" of information (whose speed is limited by that 
of light). We will return to teleportation later. 



17 

Triple Entanglement 



"Einstein said that if quantum mechanics were correct then 
the world would be crazy. Einstein was right — the world is 
crazy. " 

— Daniel Greenberger 

"Einstein's 'elements of reality' do not exist. No explana- 
tion of the beautiful dance among the three particles can be 
given in terms of an objectively real world. The particles 
simply do not do what they do because of how they are; 
they do what they do because of quantum magic." 

— Michael Home 

"Quantum mechanics is the weirdest invention of mankind, 
but also one of the most beautiful. And the beauty of the 
mathematics underlying the quantum theory implies that 
we have found something very significant. " 

— Anton Zeilinger 

"W""W7"T"hen we last left Mike Home, he was enjoying 
* JL / the fruits of the success of his work with Abner 
V V Shimony, John Clauser, and Richard Holt 
(CHSH) and the actual demonstration of entanglement by 
an experiment testing Bell's inequality, with results favoring 
quantum mechanics, carried out by Clauser and Freedman. 
The success of CHSH and its attendant experimental demon- 
strations received wide attention in the physics literature and 



203 



204 c ® ENTANGLEMENT 

made scientific news. There were expository articles pub- 
lished in journals that report on new discoveries, and there 
were new experiments and renewed excitement about the 
foundations of the strange world of the quantum. 

Soon afterwards, Clauser, Shimony, and Home got 
involved with the man who started it all: John Bell. The four 
men began an extensive communication, some appearing as 
research papers, intended to answer questions and discuss 
ideas proposed by one side or the other. This fruitful com- 
munication resulted in Bell's theorem being based on less- 
restrictive assumptions, and it also improved our 
understanding of the amazing phenomenon of entanglement. 

In 1975, Mike Home joined a research group headed by 
Cliff Shull of M.I.T., which performed experiments on neu- 
trons produced at the M.I.T. nuclear reactor in Cambridge. 
Mike spent ten years at the reactor, conducting single-parti- 
cle interference experiments with neutrons. He also met two 
physicists who would change the course of his career, and 
whose joint work with him would produce a giant leap in our 
understanding of entanglement. The two scientists were 
Daniel Greenberger and Anton Zeilinger. The three of them 
would write a seminal paper proving that three particles 
could be entangled, and would spend years studying the 
properties of such entangled triples. When, years later, I 
asked them whether the three of them were somehow "entan- 
gled" themselves, just as the triples of particles they had stud- 
ied, Anton Zeilinger quickly responded: "Yes, in fact we were 
so close that when one of us would open his mouth to say 
something, the others would finish his sentence for him ..." 



TRIPLE ENTANGLEMENT <© 20J 

Michael Home's path from two-particle interference studies 
to one-particle interference research had a good reason 
behind it. Having done the CHSH work that helped establish 
entanglement as a key principle in the foundations of quan- 
tum mechanics, Mike decided to study further problems in 
these very foundations. He knew very well the history of the 
development of ideas in the quantum theory as the discipline 
evolved. He knew that when Young did his amazing experi- 
ment with light in the 1800s and discovered the interference 
pattern that still puzzles us today, light (and other electro- 
magnetic radiation) was the only microscopic "wave" 
known. Then, of course, in 1905, Einstein proposed the pho- 
ton as a solution to the photoelectric effect, showing that 
light was not only a wave but also a stream of particles. Mike 
also knew that in 1924, de Broglie "guessed that even parti- 
cles are waves," as Mike put it, but that "no one at that time 
could perform a two-slit experiment with electrons, although 
direct confirmation of de Broglie's waves did come quickly 
from crystal diffraction of electrons." A quarter century later, 
in the 1950s, the German physicist Moellenstedt and co- 
workers did perform the experiment. They showed that these 
particles, the electrons, display the same wave-nature exhib- 
ited by an interference pattern on a screen once they emerge 
from Young's old double-slit setup. 

Then, in the mid-1970s, first Helmut Rauch in Vienna and 
then Sam Werner in Missouri independently performed what 
was essentially a double-slit experiment with neutrons. These 
massive quantum objects exhibit the same interference pat- 
terns that we associate with waves as they emerge from the 
two-slit experimental setup. The two teams, in Vienna and in 



206 C® ENTANGLEMENT 

Missouri, both used thermal neutrons: neutrons produced by 
reactions that take place inside a nuclear reactor. These neu- 
trons travel at low speeds (that is, "low" as compared with 
the speed of light) of about a thousand meters per second, 
and thus by de Broglie's formula, their associated wavelength 
is measured in a few angstroms. These very challenging 
experiments were now possible because of new semiconduc- 
tor technologies, which made available large, perfect silicon 
crystals. The scientists used hand-sized silicon crystals to con- 
struct interferometers for the thermal neutrons coming from 
the reactor. As the neutrons interacted with the crystal lattice, 
the beam of neutrons was first split by diffraction at one slab 
of the crystal, and then other slabs were used to redirect and 
eventually recombine the beams to produce the interference 
pattern. 

Mike was very interested in these experiments, which had 
just been done. He knew that Cliff Shull, one of the pioneers 
of neutron work in the 1940s (who, in 1994, would receive 
a Nobel Prize), had a lab at the M.I.T. reactor and was work- 
ing there performing experiments on thermal neutrons. Mike 
already had a position teaching physics at Stonehill College, 
but Stonehill did not have a reactor or a well-known physi- 
cist directing exciting new research. So one day in 1975, 
Mike walked into Cliff Shull's lab at M.I.T. and introduced 
himself. He mentioned to Shull his work on entanglement 
with Abner Shimony and John Clauser, and his interest in 
neutron interference experiments. Then he asked: "Can I 
play?" 

"Take that desk right there," was Shull's answer as he 
pointed to a desk on the side of the lab. From that day on, for 



TRIPLE ENTANGLEMENT <© 20J 

ten years, from 1975 to 1985, every summer, every Christmas 
vacation, and every Tuesday (the day he didn't teach), Mike 
Home spent at Shull's lab at the M.I.T. reactor doing work 
on neutron diffraction. Two experiments that he found espe- 
cially attractive had already been performed with neutrons in 
Vienna and in Missouri. Cliff Shull's group would conduct 
many more such experiments at M.I.T. 

The experiment done by Sam Werner and collaborators at 
the University of Missouri in 1975 demonstrated directly 
how neutron two-slit interference is affected by gravity — 
something that had not been shown before. There had never 
been a demonstration of the effect of gravity on quantum 
mechanical interference. The Missouri experiment was ele- 
gant and conceptually simple, and as such it demonstrated 
the essence of many of these quantum experiments. 

The two paths through the interferometer were arranged in 
the shape of a diamond. A neutron entering the diamond had 
its quantum wave split at the entrance, half the wave going 
left and half right. At the other end of the diamond, as the 
two waves recombined and exited, either a peak or a valley 
of intensity was found — just as it had on the screen of the 
classic Young's experiment, except that here this happened at 
one point rather than on a continuum of points on a screen. 
The scientists recorded whether they had found a peak or a 
trough. Then, by turning the silicon crystal, they rotated the 
diamond by ninety degrees so that it was vertical rather than 
horizontal. Now they noticed that the pattern had changed. 
The reason for this was that the two neutron waves were 
affected differently by gravity since one of them was now 
higher than the other, and a neutron at a higher level would 



208 C© ENTANGLEMENT 

travel at a lower speed. This changed the de Broglie wave- 
length along one of the paths relative to the other, and hence 
shifted the interference pattern. The experiment is demon- 
strated below. 




Detector 



Another experiment, done by Helmut Rauch and his asso- 
ciates in Vienna in 1975, an d a l so by a Missouri group that 
same year, was the 271-471 experiment with neutrons. Rauch's 
Vienna team has demonstrated using neutron interferometry 
a fascinating property of neutrons. A magnetic field was used 
to rotate the neutron in one path of the interferometer by 
360 degrees (271). Integral-spin particles — the so-called 
bosons — when undergoing a similar rotation, return to their 
original state (they've thus gone around full circle); but not 
so for the neutron. After turning around an angle of 360 
degrees, meaning going around a full circle, the neutrons 
were shown to have a sign change, which could be observed 
via the interference. Only when the magnetic field rotated 
the neutrons one more time around the circle (this is a 471 
rotation) did the neutrons return to their original state. 

In Boston, Abner Shimony and Mike Home talked during 
the same period about performing this kind of experiment 
with neutrons, aimed at proving the neutron's theoretically- 



TRIPLE ENTANGLEMENT <B 20^ 

known 271-471 quality — without knowing that Rauch and his 
students in Vienna had already performed the same experi- 
ment. Mike and Abner wrote up their paper and submitted 
it to a physics journal. But they soon discovered that the 
Vienna group had already done the same thing and had actu- 
ally performed the experiment. One of Rauch's students in 
Vienna was Anton Zeilinger. 

Anton Zeilinger was born in May 1945 in Ried/Innkreis, 
Austria. During the years 1963 to 1971, Anton studied 
physics and mathematics at the University of Vienna, receiv- 
ing his Ph.D. in physics from the university in 1971, with a 
thesis on "Neutron Depolarization in Dysprosium Single 
Crystals," written under the supervision of Professor H. 
Rauch. In 1979, Zeilinger did his Habilitation work, on neu- 
tron and solid state physics, at the Technical University of 
Vienna. From 1972 to 1981, Zeilinger was a University 
Assistant at the Atomic Research institiute in Vienna, again 
working with Rauch. 

Erice is a picturesque medieval town in Sicily. Physicists, no 
strangers to beauty and nature, have fallen in love with this 
small town in the stark, hilly surroundings of Sicily, and have 
organized annual series of conferences in this town, which 
attract physicists from all over the world. In 1976, the Erice 
conference was devoted to the foundations of quantum 
mechanics, including studies of Bell's inequalities and entan- 
glement. When he got the announcement of the meeting, 
Rauch asked Anton Zeilinger, "Why don't you go to the 
meeting? We don't know much about Bell's work, but we 
can learn and perhaps some day perform such exciting exper- 



210 C® ENTANGLEMENT 



iments, as I hear the ones involving entanglement are, right 
here in Vienna ... go and learn what you can." Anton was 
happy to comply and packed to go to Sicily. 

At the same time, in Boston, Abner, Mike, and Frank Pip- 
kin of Harvard were also packing their bags, ready to leave 
for Sicily with papers they were going to present at the meet- 
ing about their work on entanglement. Mike Home's paper 
for the meeting was the one on which he and John Clauser 
had been working for years — an extension of Bell's theorem 
to probabilistic settings. In Sicily, the Boston physicists met 
Anton Zeilinger for the first time. "We hit it off right away," 
said Mike Home. "Anton was very interested, and tried to 
learn from me everything he could about Bell's theorem. He 
was fascinated by entanglement." 

One day, back in Cliff Shull's lab at the M.I.T. nuclear 
reactor, Cliff walked over to Mike. "Do you know a person 
by the name of Anton Zeilinger?" he asked, pointing to a 
letter in his hand. "He's just applied to come here, and men- 
tioned your name in his letter." "Oh sure. Fantastic!" replied 
Mike, "He's a wonderful physicist . . . very interested in the 
foundations of quantum mechanics." 

Anton Zeilinger joined the M.I.T. team for the 1977-78 
academic year as a postdoctoral fellow, supported by a Ful- 
bright fellowship, and over the next ten years, while he was 
already a Professor in Vienna, would come to Cambridge for 
several stints, each lasting many months. He worked hard 
doing the same kind of neutron diffraction work he had done 
as a student with Rauch in Vienna, and he and Mike Home 
would co-author dozens of papers over the years, together 
with Cliff Shull and the students working with them at the 



TRIPLE ENTANGLEMENT Ca> 211 



lab at that time, the students changing from year to year. This 
pattern would last until Cliff Shull's retirement in 1987. 

Over sandwiches, while taking breaks from the lab work, 
Anton and Mike would sit together discussing two-particle 
interference, Mike's old work with Abner and John and Dick 
Holt. But their current work involved performing single-neu- 
tron interference studies. The two-particle, Bell's theorem 
ideas were now only a passionate hobby, an interest outside 
their daily work. "We would sit there, having our lunch, and 
I would fill him in on Bell's theorem, and on local hidden 
variables and how they are incompatible with quantum 
mechanics," recalled Mike Home, "and he would always lis- 
ten and want to hear more and more." 

Daniel Greenberger was born in the Bronx in 1933. He 
attended the Bronx High School of Science and was in the 
same class as Myriam Sarachik (the president-elect of the 
American Physical Society, now a colleague of Daniel's at 
CCNY), and the Nobel Prize-winning physicists Sheldon 
(Shelly) Glashow and Steven Weinberg. Danny subsequently 
studied physics at M.I.T., graduating in 1954. He then went 
to the University of Illinois to do doctoral work in high- 
energy physics with Francis Low. When Low left to take a 
position at M.I.T., Greenberger followed him, and wrote his 
dissertation at M.I.T. for his physics Ph.D. There, he studied 
mathematical physics, including the algebraic methods that 
exploit symmetries, now popular in modern theoretical 
physics. In the early 1960s, he joined Jeffrey Chew at the 
University of California at Berkeley, working on a postdoc- 
toral fellowship in high-energy physics. He then heard that 



2J2 C® ENTANGLEMENT 



the City College of New York had opened a graduate school 
with a program in physics, so he moved there in 1963, and 
has been on the faculty there ever since. 

Danny has always been fascinated by quantum theory. He 
maintains that quantum mechanics is not just a theory that 
converges with classical physics when the size of the objects 
in question increases. Rather, it is an independent theory with 
an immense richness that is not immediately apparent to us. 
Greenberger likens the quantum theory to the Hawaiian 
Islands. As we approach the islands, we only see the part that 
is above the water line: mountains and coastlines. But under 
the surface of the water there is an immense hidden dimen- 
sion to these islands, stretching all the way to the bottom of 
the Pacific Ocean. As an example demonstrating that quan- 
tum mechanics is not an extension of classical physics but 
rather has this hidden dimension, Daniel Greenberger gives 
the idea of rotation of physical objects. Angular momentum, 
he reminds us, is an element of classical physics, and has an 
analog in quantum mechanics. But spin is something that 
exists only for microscopic objects that live in the quantum 
world and has no analog in classical physics. 

Greenberger was interested in the interplay between rela- 
tivity theory and quantum mechanics. In particular, he 
wanted to test whether Einstein's important principle of the 
equivalence of inertial and gravitational mass was true at the 
quantum level. To do so, he realized, he would need to study 
quantum objects that were also affected by gravity. One such 
object, he knew, was the neutron. Physicists have always 
looked for the connection between general relativity, which 
is the modern theory of gravity, and the quantum world. 



TRIPLE ENTANGLEMENT © 2J3 

Neutrons are quantum elements because they are small; but 
they are also affected by gravity. So perhaps the connection 
between these theories might be found by studying neutrons. 

Greenberger contacted the scientists working at the 
research reactor of the Brookhaven National Laboratory on 
Long Island about doing neutron research, but was told that 
they did not do interference studies with neutrons. He found 
out, however, that Cliff Shull at M.I.T. did do such research, 
and in 1970 Danny traveled to Cambridge to meet him. Five 
years later, he saw an article by Colella, Overhauser, and 
Werner about the Aharonov-Bohm Effect, and he contacted 
Overhauser and exchanged ideas with him about the effect. 
Danny realized there was an aspect that needed to be 
explored. Later he published a paper about the effect in the 
Review of Modern Physics. In 1978, there was a conference 
on these topics in physics at the large nuclear reactor in 
Grenoble, France. Overhauser, who was invited to attend the 
conference, couldn't go and asked Greenberger if he would 
go there instead. 

At Grenoble, Danny met Anton Zeilinger, who at that time 
was working at the Grenoble reactor of the Institut Laue- 
Langevin as a part-time Guest Researcher. And he also met 
Mike Home, who, like Danny, was attending the conference. 
Since Greenberger, Home, and Zeilinger were all interested in 
the same topic, a bond was established among them. "That 
meeting changed my life," recalled Greenberger. "The three of 
us really hit it off together. " From Grenoble, Anton went back 
to Austria, to continue his research there, and upon his return 
to M.I.T, he was pleased to find that Danny Greenberger had 
also joined the M.I.T. team, for a short visit. But the visit 



214 c ® ENTANGLEMENT 

would repeat itself over and over again for many years — up 
until Cliff Shull's retirement in 1987 — allowing the three sci- 
entists to work closely together. Even after Cliff's retirement, 
an N.S.F. grant together with Herb Bernstein of Hampshire 
College allowed them to continue their investigations. 

Anton would come to M.I.T. for stays of several months, 
sometimes years, each; Danny would come for short visits 
of a few weeks at a time. The exception was Danny's long 
stay in 1980, when he had a sabbatical leave. The three 
physicists quickly became a close-knit group within the larger 
community of scientists doing work at the M.I.T. reactor, 
and they spent many hours outside the lab talking about 
entanglement, a topic of great interest to all of them. While 
at the lab they worked exclusively on one-particle (neutron) 
interference, many of their off-lab discussions centered on 
two-particle interference and Bell's magical theorem. 

The entanglement among the three physicists was com- 
plete. Danny and Mike simultaneously noticed some theo- 
retical puzzles concerning the famous Aharonov-Bohm effect 
of the 1950s and independently did work on the problem. 
Danny Greenberger wrote up his findings and published 
them in a journal. Anton and Danny would come up with 
closely related ideas about physics; and the same would hap- 
pen between Mike and Anton, who for ten years would write 
joint papers about their research on one-particle interferom- 
etry based on their work at Shull's lab. In 1985, Mike and 
Anton produced a joint paper on entanglement that proposed 
an experiment to demonstrate that the phenomenon exists 
also for the positions (in addition to spin or polarization) of 
two particles, and that Bell's theorem would apply here too. 



TRIPLE ENTANGLEMENT <© 21 J 

One day in 1985, Anton and Mike came across an 
announcement for a conference in Finland organized to cel- 
ebrate the fiftieth anniversary of the Einstein, Podolsky, and 
Rosen (EPR) paper and the revolution in science it has 
spawned. They decided that it would be great to go to Fin- 
land, but needed a paper on two-particle interference to pres- 
ent at the conference; their single-particle research would not 
have been suitable. In a few days they had a double-diamond 
design for a new type of experiment to test Bell's inequality. 
This became their paper for the meeting. The idea was to 
produce entangled photons and then perform an interference 
experiment with these photons, using the double diamond. 
Their design is shown below. 




In this experimental design, a specialized source simulta- 
neously emits two particles, A and B, traveling in opposite 
directions. Thus the pair can go through either holes a and fe, 
respectively, or through holes cf and b\ Suppose that parti- 
cle B is captured at one of the detectors monitoring holes b 
and b\ If particle B lands at ft, then we know that particle A 
is taking hole a. Similarly, if particle B lands in b\ then we 
know that A is taking hole a\ Thus, for every 100 pairs pro- 



2l6 C® ENTANGLEMENT 

duced by this source, the two upper detectors will each reg- 
ister 50 "A" particles; i.e., there is no single particle inter- 
ference here, because access to particle B can reveal which 
path particle A takes. In fact, it is not even necessary to insert 
the detectors near holes b and b'; just the fact that we could 
determine which hole particle B takes is enough to destroy 
the single-particle interference for particle A. 

So imagine that the detectors near b and b' are removed 
and the two upper ("A") and the two lower ("B") detectors 
are monitored while 100 pairs are emitted by the source. 
Quantum mechanics predicts that every detector will count 50 
particles; i.e., there is no single-particle interference for either 
A or B because we could determine the route of either parti- 
cle by catching the other one near the source. But quantum 
mechanics does predict amazing correlations between the 
counts. If B lands in the lower left detector, then A will cer- 
tainly land in the upper right detector; if B is found in lower 
right, then A will land in the upper left detector. Lower left 
and upper left detectors never fire together, and neither do the 
lower right and upper right detectors. However, if we move 
one of the beam splitters an appropriate distance left or right, 
the correlations will change completely. The two left and the 
two right detectors now fire in coincidence, but detectors diag- 
onally across from each other now never fire together. But 
still the count rate at each separate detector remains a steady 
50, independently of the positions of the beam splitters. This 
behavior is explained quantum mechanically by saying that 
each pair of particles is emitted through both holes a and ft, 
and through both holes a 3 and b\ This mysterious quantum 
state is an example of two-particle entanglement. 31 



TRIPLE ENTANGLEMENT <© 2IJ 

One day, while sitting in Mike Home's kitchen, Danny 
Greenberger asked him: "What do you think would happen 
with three-particle entanglement?" The question was, first 
of all, what are the details of three-particle correlations? The 
question was also: How might EPR's assumptions deal with 
three entangled particles? Would there be any special diffi- 
culties in trying to give a local realistic account of entangle- 
ment, or would the conflict between quantum mechanics and 
Einstein's locality be essentially the same as with two parti- 
cles? Danny became convinced that this was a very worth- 
while line of research to pursue during his upcoming 
sabbatical year. And, looking ahead to possible experiments, 
he recalled that in the Wu-Shaknov setup of positronium 
emission, as the two particles annihilated each other, usually 
two high-energy photons were emitted; but, according to the 
probability laws of quantum mechanics, every so often three 
photons would have to be emitted as well. This was a possi- 
ble experimental setup to keep in mind during the new 
research project. Mike Home thought about Danny's ques- 
tion, and replied, "I think that would be a great topic to pur- 
sue." Greenberger went home, and thought about the 
problem. Over the next few months, he would contact Mike 
and say: "I'm getting great results with three-particle entan- 
glement — I have inequalities popping up everywhere; I think 
that three-particle entanglement may be a greater challenge 
to EPR than two-particle entanglement." Mike was inter- 
ested, but also knew that Bell's theorem and the experiments 
had already proven EPR wrong, and hence there was no 
pressing need for another proof. But he was interested 
enough in the physics of three-particle entanglement to dis- 



218 Cs ENTANGLEMENT 

cuss the situation with Danny and encouraged him to 
continue. 

In 1986, while Anton was back in Vienna working with 
Rauch, Danny was awarded a Fulbright fellowship, which 
allowed him to travel to Europe for his sabbatical year. He 
decided to use the opportunity to join Anton and work with 
him in Austria. The issue of three-particle entanglement 
remained very much on his mind as he traveled across the 
Atlantic. When he arrived in Vienna, Danny already had 
some very good ideas. He was close, he felt, to getting Bell's 
theorem without inequalities. In Vienna, Anton and Danny 
shared an office, and Danny would always show Anton his 
developing theoretical results, and the two of them would 
discuss them at length. Finally, Danny Greenberger had in 
front of him a situation in which a perfect correlation among 
three particles was enough to prove Bell's theorem. No 
longer was there a need to search with a partial correlation 
between two photons, as had been done experimentally by 
Clauser and Freedman, Aspect, and others. Here was a 
tremendously powerful — and yet conceptually simpler — 
proof of Bell's theorem. "Let's publish it!" said Danny, and 
Anton added that he and Mike had done some joint, related 
work that should be included in the same paper. The two 
conferred with Mike Home in Boston over the phone, and 
decided to work on a paper on the subject. 

In 1988, Mike was leafing through an issue of the journal 
Physical Review Letters at Shull's lab and noticed a paper 
by Leonard Mandel. The paper had an almost identical 
experimental design to the one he and Anton had proposed 



TRIPLE ENTANGLEMENT <B 2I<) 

earlier in their presentation in the Finland conference. The 
only difference was that Mandel's two-particle interference 
design was a folded diamond, rather than a straight one as in 
the Horne-Zeilinger figure. But Mandel, who had not seen 
the proceedings of the Finland conference, had actually done 
the experiment as well; he used the down-conversion method 
for producing entangled photons. Thus two-particle inter- 
ference was not only a thought experiment, but the real 
thing. And, moreover, Bell experiments could now be done 
with beam entanglement and without spin or polarization. 
Since Anton and Mike had only presented their proposal 
of two-particle interference, and of Bell experiments without 
polarization, at conferences, and since their understanding 
of the entanglement basis for the interference was different 
and simpler than Mandel's, they decided to publish a Physi- 
cal Review Letter presenting their results. Abner joined them 
in this write-up. Since the paper was essentially a comment 
on Mandel's breakthrough experiment, Mandel himself was 
assigned by the journal to be the referee. A long period of 
activity and cooperation followed, in which two-particle 
interferometry using down-conversion was pursued by the 
Boston team, Mandel at Rochester, Shih in Maryland, and 
others. 

Having decided in 1986 to work together on an article on 
three-particle entanglement, Anton, Mike, and Danny some- 
how left the writing project dangling and continued their 
usual work. Danny Greenberger left Vienna and traveled in 
Europe. Eventually, his sabbatical year over, he returned to 
New York and to his regular teaching work. Nothing was 



220 C® ENTANGLEMENT 



done with the exciting new results on three-particle entan- 
glement for two years. Then, in 1988, Danny was awarded 
an Alexander von Humboldt fellowship to do research in 
Garching, Germany, at the Max Planck Institute, where he 
would spend eight months as a visiting researcher. While 
there, he called Anton in Vienna. "Now I have the time to 
write ..." he said. "I already have seventy pages," he said, 
"and I haven't even begun!" But the formal writing of the 
paper didn't proceed. Danny traveled throughout Europe, 
giving talks about his work with Anton and Mike on the 
properties of three entangled particles and how they related 
to Bell's theorem and EPR. At the end of the summer of 
1988, Danny Greenberger went to the Erice, Sicily conference 
of that year. He gave a talk about three-particle entangle- 
ment, and Cornell's David Mermin — another quantum 
physicist — was in the audience. According to Danny, his 
sense was that the paper didn't really catch Mermin's 
attention. 

But when he returned home to New York, Danny began to 
receive papers from several groups of physicists making ref- 
erences to his own work with Mike and Anton. One of these 
groups of physicists was headed by Michael Redhead of 
Cambridge University. The Redhead group claimed to have 
improved the Greenberger-Horne-Zeilinger work on three- 
particle entanglement, which Danny had presented at Erice 
and elsewhere in Europe. Danny called Anton and Mike: 
"We must do something soon," he said. "People are already 
referring to our work without it ever having been published." 

In 1988, Danny presented a paper, which was published in 
the proceedings of a physics conference at George Mason 



TRIPLE ENTANGLEMENT Ca> 22J 



University. Meanwhile, David Mermin received the Redhead 
paper, which referred to the work by Greenberger, Home, 
and Zeilinger. For his "Reference Frame" column in the mag- 
azine Physics Today, Mermin wrote an article titled "What's 
Wrong with These Elements of Reality?" Physics Today is 
the news magazine of the American Physical Society, and 
hence the paper received wide distribution. The physics com- 
munity became fully aware of the new findings, referring to 
them as "GHZ entanglement" — even though the anticipated 
paper by Greenberger, Home, and Zeilinger had still not 
been published. (In many sciences, a paper included in the 
proceedings of a conference does not count as much as a 
paper published in a refereed journal.) In fact, two of the 
paper's authors did not even know that a paper bearing their 
names had been presented at a conference and published in 
the proceedings. Danny had forgotten to mention this fact to 
them. 

One day Abner said to Mike: "What is this thing that you 
and Danny and Anton proved?" "What thing?" asked Mike 
Home. Abner handed him the paper by David Mermin. Mer- 
min clearly attributed the proof he was describing, showing 
that quantum mechanics was incompatible with hidden vari- 
ables in a strong sense in the case of three entangled particles, 
to Greenberger, Home, and Zeilinger. Before he knew it, 
Mike was getting correspondence from the physics commu- 
nity congratulating him on the success of GHZ. On Novem- 
ber 25, 1990, John Clauser wrote Mike Home a card from 
Berkeley: 



222 <n> ENTANGLEMENT 

Dear Mike 

You old fox! Send me a (p)reprint of GHZ. Mermin seems to 
think this is super-hot stuff. 

The congratulations included some from people at the top of 
the profession, including Nobel Prize winners. The three 
physicists quickly realized that they had better put their 
research in a proper journal. To do so, they invited Abner 
Shimony to join them, since he had been doing Bell work 
from the beginning. In 1990, the paper, "Bell's Theorem 
Without Inequalities," by Greenberger, Home, Shimony, and 
Zeilinger, was published in the American journal of Physics, 
although the idea of three-particle entanglement and the 
improved Bell theorem continues to be called GHZ. 32 

The three-particle arrangement for presenting the GHZ 
theorem can be either a spin or polarization version of the 
experiment, or it can be a beam-entanglement version. The 
polarization version of the GHZ experimental arrangement 
is shown on page 224. 

The most amazing thing about three-particle entanglement, 
and the main reason for the interest taken in the GHZ pro- 
posal, is that it can be used to prove Bell's theorem without 
the cumbersome use of inequalities. 

The question remained: how to create three entangled pho- 
tons in the laboratory? This can be achieved by a truly 
bizarre quantum property, as was shown in a proposal by 
Zeilinger and coworkers in 1997. The design is shown here. 

If two pairs of entangled photons are brought into a cer- 
tain experimental arrangement that makes one member of 
one pair indistinguishable from one member of the other pair, 



TRIPLE ENTANGLEMENT © 223 

and one of the two newly-indistinguishable photons is cap- 
tured, then the remaining three photons become entangled. 
What is so incredible here is that the photons become entan- 
gled because an outside observer can no longer tell which 
pair produced the captured photon. Then, leaving out the 
captured photon, the remaining three are entangled. 
Zeilinger and collaborators actually produced such an 
arrangement in 1999. 



d + 



^ 




"^' 







" BS 



There are accessible versions of the GHZ proof of Bell's the- 
orem using three entangled photons. David Mermin, GHZ 
themselves, and, recently in a textbook, Daniel Styer have 
presented the argument in forms suitable for a general 
audience. 

These arguments are accessible for two common reasons. 
First, the quantum predictions are not derived but simply 
reported, thereby sparing the reader the mathematical deri- 
vations. Second, not all of the quantum predictions are 
reported, only the ones needed for the argument. The fol- 
lowing version is by Mike Home, who used it in May 2001 
in his Distinguished Scholar Lecture given to the Stonehill 
College faculty and students. It borrows much from the ear- 
lier arguments, with the additional simplification that it uses 
the beam-entanglement version of GHZ, thereby avoiding 



224 c ® ENTANGLEMENT 

spin or polarization. The argument is adapted from Mike's 
presentation with the kind permission and help of its author. 
The figure below shows the beam-entangled GHZ setup, 
which clearly is a straightforward generalization of the two- 
particle interferometry to three particles. A half-silvered mir- 
ror at each of three locations may be set to one of two 
positions, the left (L) position, or the right (R) position. 
Depending on these settings, experimental outcomes change. 

i 

/BS X 



/sa. 




The figure shows an arrangement in which a very special- 
ized source in the center of the figure emits three entangled 
particles simultaneously. Since these particles (or photons) 
are quantum objects, and they are entangled, each triple of 
particles goes both through holes a, b, and c, and through 
holes a\ b\ and c\ As they travel through the triple-diamond 



TRIPLE ENTANGLEMENT <© 22J 

design, each particle encounters a beam-splitter (1/2-silvered 
mirror), which can be at either the L or the R position. 

Quantum mechanics predicts that, for each particle, the 
+ 1 and the -1 results (which are analogous to spin "up" or 
"down" for a particle, or polarization direction vertical or 
horizontal for a photon) occur with equal frequency: half the 
time +1 and half the time -1, independently of the positions 
of all beam splitters. If we look at pairs of particles, we still 
will see no interesting pattern: all pairs of results (+1, +1), 
(-1, -1), (+1, -1), and (-1, +1) will occur with equal frequency 
(1/4 of the time each) for both particles A and B (and simi- 
larly for the other pairs, B and C and A and C), indepen- 
dently of the positions of the beam splitters. However, 
quantum mechanics predicts that an observer will see a truly 
magical dance if the observer should look at what happens to 
all three particles. For example, quantum mechanics predicts 
that if the beam splitters for particles B and C are both set in 
the L position, and both of these particles land in, say, the 
-1 outcome detectors, and if the particle A beam splitter is set 
to the R position, then particle A will land in the +1 detector 
with certainty. This is a remarkably strong prediction, and 
there are similar perfect predictions for other combinations 
of settings. The table below summarizes the combinations of 
settings and the quantum mechanical predictions. 



ZZ6 C® ENTANGLEMENT 

For beam splitter settings: The quantum mechanical 

predictions are: 
ABC 

1. R L L Either o or 2 particles 

will go to -l 

2. L R L Either o or 2 particles 

will go to -1 

3. L L R Either o or 2 particles 

will go to -1 

4. R R R Either 1 or 3 particles 



will go to 



1 



Other setting combinations (for example, LLL) are not needed 
in our discussion. 

The predictions on the right for the particular setting com- 
binations on the left were obtained by Greenberger, Home, 
Shimony, and Zeilinger using the mathematics of quantum 
mechanics. They began, of course, with the actual entangle- 
ment state of the three particles. The idea of entanglement is 
a superposition of states, as we know, and for three parti- 
cles, each going through two apertures, we have the super- 
position state that can be written (in a somewhat simplified 
form) as: 

(abc + a'b'c') 

This equation is the mathematical statement of three-particle 
entanglement, in which the "+" sign captures the both-and 
property mentioned earlier. 

From the equation, which describes the superposition of 
the states — i.e., describes mathematically exactly what it 



TRIPLE ENTANGLEMENT <© 227 

means for three particles to be entangled, within the specific 
setting of this experiment with its six holes — the physicists 
worked out the mathematics and derived the predictions, 
listed in the table above. The actual details can be found in 
the appendix to the paper "Bell's Theorem Without Inequal- 
ities," by Greenberger, Home, Shimony, and Zeilinger, Amer- 
ican journal of Physics, 58 (12), December 1990. Note that 
even in their scientific paper, the authors relegated their alge- 
braic derivation of the quantum mechanical predictions 
based on the state equation to an appendix — it was just too 
long, and it is elementary quantum mechanics. The interested 
(and mathematically inclined) reader may look for these 
details there. What is important for the reader to understand 
is that the predictions in the table above are exactly what 
quantum mechanics tells us will happen in each situation. 
There is nothing more in these predictions than an applica- 
tion of the rules of quantum mechanics to a particular setting 
and the state of entanglement of the three particles. We will 
therefore take these predictions as valid, direct consequences 
of the entanglement of the three particles. 

Going back to our table of the quantum mechanical pre- 
dictions for the three-particle entangled state, we find that: 
Given the beam-splitter settings, and given specific outcomes 
for B and C, the outcome for particle A is predictable with 
certainty. For example, suppose that the beam-splitters for 
particles B and C are both in the L position, and that parti- 
cle B lands in the -1 detector and C also lands in -1. Then, if 
the particle A beam-splitter is in the R position, particle A 
will certainly go to detector +1. There are similar perfect cor- 
relations, as can be seen from the table above, for other 



22tf C® ENTANGLEMENT 



choices of beam-splitter settings and other outcomes at two 
stations. In short, given the beam-splitter settings and specific 
outcomes for B and C, the outcome for particle A is pre- 
dictable with certainty. 

Now comes the important part of the work of GHZ. To 
understand what it is, and why the GHZ state provides such 
a powerful demonstration and extension of Bell's theorem, 
we have to go back to what Einstein and his colleagues said 
fifty-five years earlier, in the EPR paper of 1935. 

Einstein and his coworkers noted the strikingly perfect cor- 
relations present in a theoretical two-particle entanglement. 
They argued that these perfect correlations are perplexing — 
unless they simply reveal pre-existing, objectively-real prop- 
erties of the entangled objects. Einstein and his colleagues 
stated their commitment to the existence of an objective real- 
ity as follows (in the EPR paper of 1935): 

"If, without in any way disturbing a system, we can predict 
with certainty the value of a physical quantity, then there 
exists an element of physical reality corresponding to this 
physical quantity." 

Now, the landing of particle A in its +1 detector is an "ele- 
ment of reality" as per Einstein's definition, because we can 
predict that this will happen with certainty, and clearly we 
did not disturb particle A by our choice of beam splitter set- 
tings at the distant locations B and C. The outcome at A can 
at most depend on the beam splitter setting at station A, not 
at B or C. Now, since the landing of particle A in detector +1 
is an "element of reality," let's call this element of reality 
A(R). Thus, A(R) is the element of reality at location A. It sig- 
nifies the outcome at station A when the beam splitter that 



TRIPLE ENTANGLEMENT <B 22£ 

controls particle A is set to the right (R) setting. For the spe- 
cific outcome that particle A lands in the +1 detector, we say 
that the element of reality is +1 and write it as: A(R)=+i. 
Similarly for other locations and settings combinations, we 
have, following Einstein, six elements of reality: A(R), B(R), 
C(R), A(L), B(L), and C(L). Each of these elements of reality 
has a value of either +1 or -1. 

Now comes the GHZ Theorem: 

Assume that Einstein's elements of reality do exist and 
can explain the otherwise baffling quantum mechanical pre- 
dictions given in the table above (and which, by now, have 
been experimentally verified by an actual 3 -particle entan- 
glement experiment conducted by Zeilinger in 1999). 
Agreement with quantum predictions 1, 2, 3, and 4 of the 
table above imposes the following constraints on the ele- 
ments of reality: 

1. A(R) B(L) C(L)= +1 

2. A(L) B(R) C(L)= +1 

3. A(L) B(L) C(R)= +1 

4. A(R) B(R) C(R)= -1 

The above statements are true because of the following. In 
case (1), the settings are RLL and, according to quantum 
mechanics, as listed in the table earlier, "Either o or 2 parti- 
cles go to -1." Thus either o or two of the elements of real- 
ity A(R), B(L), and C(L) are equal to -1. And when you 
multiply all three of them, you will thus get: 1x1x1 = 1 (in the 
case o of them go to -1) or ix(-i)x(-i)=i (for the case that 2 
particles go to -1; regardless of order). Similarly, for cases (2) 



230 Cs ENTANGLEMENT 

and (3) we also get that the product of the elements of real- 
ity is equal to 1, either because all three of them are equal to 
1 (o particles go to -1), or because any two of them are -1 (the 
case that 2 particles go to -1) and the third is a +1. 

In case (4), the quantum mechanical prediction is that 
either 1 particle or 3 particles go to -1. Thus the possible 
products of the three elements of reality A(R) B(R) and C(R) 
are: 

-1 times two +is, or three -is multiplied together. In either 
case, the product has an odd number of -is and the answer 
therefore is -1. 

Now comes the great trick: Multiply together the top three 
equations. Multiplication of the left sides gives us: 

A(R) A(L) A(L) B(L) B(R) B(L) C(L) C(L) C(R) = A(R) B(R) C(R) 

The reason that this is true is that each of the terms excluded 
from the right side of the equation appears twice on the left 
side of the equation. Each of the terms A(L), B(L), C(L) has 
a value of either +1 or -1; when such a term appears twice in 
the equation, the product of the term times itself is certainly 
equal to +1 (because +ix+i=+i and -ix-i=+i). 

Now, multiplying the right sides of the equations (1), (2), 
and (3) we get +ix+ix+i=+i; so that we have: A(R) B(R) 
C(R) = +i. 

But our quantum mechanical prediction, equation (4), says 
that: A(R) B(R) C(R) = -1. 

Thus we have a contradiction. Therefore, Einstein's "ele- 
ments of reality" and locality could not possibly exist if 
quantum mechanics is correct. Hidden variables are impos- 
sible within the framework of quantum mechanics. The 



TRIPLE ENTANGLEMENT C® 231 

entangled particles do not act the way they do because they 
were "pre-programmed" in any way: such programming is 
impossible if particles behave according the rules of the quan- 
tum theory. The theorem shows that any instruction sets the 
particles might possess must be internally inconsistent, and 
hence impossible. The particles respond instantaneously 
across any distance separating them in order to give us the 
results that quantum theory says will be obtained. This is the 
magic of entanglement. 

Furthermore, actual experiments have shown that the 
quantum theory is correct, and therefore Einstein's local real- 
ism is not. The GHZ theorem proves the contradiction in a 
much more direct, easier to understand, and non-statistical 
way, as compared with Bell's original theorem. 

"In all our work, there has never been any competition. It's 
been wonderful," recalled Mike Home when describing to 
me his work with his colleagues in coming up with the GHZ 
design and the discovery of the GHZ triple-particle entangled 
state. "We were fortunate to work in a field in which very few 
people were working, and thus everyone welcomed others 
who were excited about the same problems in the founda- 
tions of quantum mechanics," he said. 

These physicists, working together in harmony, produced 
one of the most important contributions to modern physics. 
Their work would be expanded and extended in the follow- 
ing years, and it would help spawn new technologies, which 
could only have been imagined by science fiction writers only 
a few years earlier. 



232 Cs ENTANGLEMENT 

The Borromean rings are named after the Borromeo family, 
whose members belong to the Italian nobility. The family 
owns the beautiful Borromean Islands on Lake Maggiore in 
northern Italy. The family coat of arms consists of three rings 
intertwined in an interesting way: should one of them be bro- 
ken, the other two will no longer remain linked as well. The 
rings may represent the idea of "united we stand, divided we 
fall." The physicist P.K. Aravind has studied entanglement 
and has discovered connections between entangled stated in 
quantum mechanics and various kinds of topological knots. 
In particular, Aravind has argued that there is a one-to-one 
correspondence between the GHZ entangled state of three 
particles and the Borromean rings. The Borromean rings are 
shown below. 33 




Aravind's proof has to do with entanglement along a par- 
ticular direction of spin (the z-direction). He's also shown 
that if one measures the spin of three entangled particles 
along another direction, the x-direction, then the entangled 
state is different. Now it is no longer analogous with the Bor- 
romean rings, but rather with the Hopf rings. Three Hopf 



TRIPLE ENTANGLEMENT <B 233 

rings are interlocked in such a way that if one of them is cut, 
the other two remain locked together. Three Hopf rings are 
shown below. 




Aravind has also demonstrated that a general, w-particle 
GHZ state of entanglement could be viewed as a generaliza- 
tion of the three Borromean rings. Such a linking of several 
particles is analogous to a linked chain that looks like the 
rings below. 




Danny Greenberger still spends time alternately visiting 
Mike Home in Boston and Anton Zeilinger in Vienna, thus 



234 <*» ENTANGLEMENT 

keeping alive the entanglement among these three good 
friends. In Austria, Danny spends time with Anton's research 
group at the University of Vienna — a key group conducting 
leading-edge work on a wide array of quantum behavior and 
entanglement, including teleportation. Recently, Danny 
attended a party given by the research group. There he met 
Schrodinger's daughter, and, by her side, Schrodinger's 
grandson — by another mother. The young man, a member 
of the research group, had not found out that the great physi- 
cist was his grandfather until he became an adult and a quan- 
tum physicist himself. 



i8 

The Ten-Kilometer Experiment 



"If two separated bodies, each by itself known maximally, 
enter a situation in which they influence each other, and 
separate again, then there occurs regularly that which I 
have just called entanglement of our knowledge of the two 
bodies." 

— Erwin Schrodinger 



The next chapter in the history of the mysterious phe- 
nomenon of entanglement was written by Nicholas 
Gisin of the University of Geneva. Gisin was born in 
Geneva in 1952 and studied theoretical physics at the Uni- 
versity of Geneva, obtaining his Ph.D. in this field. He was 
always interested in the mystery of entanglement. In the 
1970s, he met John Bell at CERN, and was very much taken 
with the man, later describing him as sharp and impressive. 
Gisin immediately recognized Bell's work as a groundbreak- 
ing achievement in theoretical physics. Gisin wrote a number 
of theoretical papers on Bell's theorem, proving important 
results about quantum states. He then spent some time at the 
University of Rochester, where he met some of the pioneers 
in optics research: Leonard Mandel, whose work made him 
a legend in the field, and Emil Wolf. 



235 



2 3^ 



ENTANGLEMENT 



Nicholas then returned to Geneva and worked in industry 
for four years. This was a fortuitous move since it allowed 
him to combine his passion for quantum mechanics with 
practical work with fiber optics. The link he forged between 
fiber optics technology and quantum theory would prove 
crucial for the new work on entanglement. Equally important 
would be the connections he established with telephone 
companies. Returning to the University of Geneva, Gisin 
began to design experiments to test Bell's inequality. 

By that time, the 1990s, Clauser and Friedman and others 
had established the first experimental violation of Bell's 
inequality and Alain Aspect had taken the work further than 
anyone by establishing that any signal from one point of the 
experimental setup to the other would have had to travel at 
a speed faster than light, thus establishing that no such sig- 
nal could have been received. Aspect's experiment was done 
within the space of a laboratory. Following Aspect's experi- 
ments, Anton Zeilinger and collaborators have extended the 
range at which entanglement was tested to hundreds of 
meters, across several buildings around their laboratory in 
Austria. This setup is shown below. 



^ £p*£*c£*&> & 




200 m 



200 m 



But Gisin wanted to go much farther. First, he designed an 
experiment by which entangled photons traveled a distance 
of 3 5 meters, inside his laboratory. 



THE TEN-KILOMETER EXPERIMENT & 2^J 



His connections with the telephone companies allowed 
him to enlist their enthusiastic support for an ambitious 
experiment. The scale of the work would be unprecedented: 
Gisin conducted his photon experiment not in air but within 
a fiber-optical cable. And the cable was laid from one loca- 
tion to another, 10.9 kilometers (seven miles) away as the 
crow flies. Counting the actual distance traveled, with all the 
bends and curvature of the cable, one reaches a total distance 
of 16 kilometers (ten miles). Gisin came to the experiment 
with an open mind. He would have found either outcome 
fascinating: a confirmation of quantum mechanics or a result 
supporting Einstein and his colleagues. The result was an 
overwhelming affirmation of entanglement, the "spooky 
action at a distance," which Einstein so disliked. Bell's 
inequality was once again used to provide strong support for 
nonlocality. Because of the experimental setup, a signal from 
one end of the cable to the other, telling one photon what 
setting the other photon found, would have had to travel at 
ten million times the speed of light. The map of the experi- 
ment is shown below. 



Bellevue 




classical channels 



Bern ex 



23 8 C© ENTANGLEMENT 

Like some other physicists, Gisin believes that while entan- 
glement doesn't allow us to send readable messages faster 
than light, the phenomenon still violates the spirit of special 
relativity. He thus wanted to test the entanglement phenom- 
enon within a relativistic framework. In one of his experi- 
ments, Gisin used an absorbing black surface, placed at the 
ends of the optical fiber, to collapse the wave function. The 
two ends of the fiber through which entangled photons were 
to appear were again placed kilometers apart, but the absorb- 
ing surfaces were moved at extremely high speeds. By manip- 
ulating these experimental conditions, it was possible to study 
the entanglement phenomenon using different relativistic ref- 
erence frames. Thus time itself could be manipulated in accor- 
dance with the special theory of relativity: each photon could 
be measured as arriving at its endpoint at different times. 
First, one member of a pair of photons was the first one to 
arrive at its target, and in the second experiment its twin 
arrived before it. This complex experiment using moving ref- 
erence frames resulted in a strong confirmation of nonlocal 
entanglement and the predictions of quantum mechanics. 

In the 1990s, the big news in quantum technology was cryp- 
tography. The idea of using entanglement in quantum cryp- 
tography was put forward by Arthur Ekert of Oxford 
University in 1991. The term is a bit of a misnomer since 
cryptography is the art of encrypting messages. Quantum 
cryptography, however, usually means techniques for evading 
and detecting eavesdroppers. Entanglement plays an impor- 
tant role within this new technology. Gisin's associates at the 
Swiss telephone companies were very interested in this kind 



THE TEN-KILOMETER EXPERIMENT C© 239 

of research, since it could allow for the development of secure 
communications networks. He performed research in quan- 
tum cryptography, and in one of his recent experiments was 
able to transmit secure messages a distance of 25 kilometers 
(16 miles) under the water of Lake Geneva. Gisin is enthusi- 
astic about his great achievements in cryptography, both 
using entanglement and using other methods. He believes 
that the field has matured and that quantum cryptography 
could be used commercially at distances such as the ones used 
in his experiments. Gisin has also spent time in Los Alamos, 
where an American team of scientists is making progress on 
quantum computing, another proposed new technology 
that — if successful — would use entangled entities. 



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19 

Teleportation: 
'Beam me up, Scotty!" 



"Entanglement — along with superposition of states — is the 
strangest thing about quantum mechanics." 

—William D. Phillips 



Quantum teleportation has until recently been only 
' a thought experiment, an idea that had never 
been successfully tested in the real world. But in 
1997, two teams of scientists were successful in 
realizing the dream of teleporting a single particle's quantum 
state. 

Quantum teleportation is a way of transferring the state of 
one particle to a second particle, which may be far away, 
effectively teleporting the initial particle to another location. 
In principle, this is the same idea — at this point existing only 
within the realm of science fiction — by which Captain Kirk 
can be teleported back into the spaceship Enterprise by 
Scotty, who is aboard the spaceship. 

Teleportation is the most dramatic application we can 
imagine of the phenomenon of entanglement. Recently, two 



241 



242 Cs ENTANGLEMENT 

international teams, one headed by Anton Zeilinger in 
Vienna, and the other headed by Francesco De Martini in 
Rome, brought the idea of teleportation from the imagina- 
tion to reality. They followed a suggestion made in 1993 by 
Charles Bennett in an article in a physics journal. Bennett 
showed that there was a physical possibility of teleporting 
the quantum state of a particle. 

The reason physicists began to think about teleportation 
was that in the 1980s it was shown by William Wootters and 
W. Zurek that a quantum particle can never be "cloned." 
The No Cloning Theorem of Wootters and Zurek says that 
if we have a particle, its state cannot be copied onto another 
particle, while the original particle remains the same. Thus, 
it is impossible to create a kind of copying machine that 
would take one particle and imprint its information onto 
another particle, keeping the original intact. Thus the only 
way that physicists could conceive of imprinting information 
from one particle onto another was by having the same infor- 
mation disappear from the original particle. This hypotheti- 
cal process was later given the name teleportation. 

The paper describing the dramatic teleportation experi- 
ment of Zeilinger's team, "Experimental quantum telepor- 
tation," by D. Boumeester, J.-W. Pan, K. Mattle, M. Eibl, H. 
Weinfurter, and A. Zeilinger, appeared in the prestigious jour- 
nal Nature in December 1997. It says: 

"The dream of teleportation is to be able to travel by sim- 
ply reappearing at some distant location. An object to be tele- 
ported can be fully characterized by its properties, which in 
classical physics can be determined by measurement. To 
make a copy of that object at a distant location one does not 



TELEPORTATION: "BEAM ME UP, SCOTTY" &> 243 

need the original parts and pieces — all that is needed is to 
send the scanned information so that it can be used for recon- 
structing the object. But how precisely can this be a true copy 
of the original? What if these parts and pieces are electrons, 
atoms and molecules?" The authors discuss the fact that 
since these microscopic elements making up any large body 
are given to the laws of quantum mechanics, the Heisenberg 
uncertainty principle dictates that they cannot be measured 
with arbitrary precision. Bennett, et al., suggested the idea of 
teleportation in an article in Physical Review Letters in 1993, 
proposing that it may be possible to transfer the quantum 
state of a particle to another particle — a quantum teleporta- 
tion — provided that the person doing the teleportation does 
not obtain any information about the state in the process. 

It seems absurd that any information obtained by an out- 
side observer should affect what goes on with a particle, but 
according to quantum mechanics, the mere process of observ- 
ing a particle destroys (or "collapses") the wave-function of 
the particle. Properties of momentum and position, for exam- 
ple, cannot be known to any given precision. Once measured 
(or otherwise actualized), a quantum object is no longer in 
that fuzzy state in which quantum systems are, and infor- 
mation is thus destroyed in the process of being obtained. 

But Bennett and his coworkers had a brilliant idea as to 
how one might transfer the information in a quantum object 
without measuring it, i.e., without collapsing its wave-func- 
tion. The idea was to use entanglement. Here is how tele- 
portation works. 

Alice has a particle whose quantum state, unknown to her, 
is Q. Alice wants Bob, who is at a distant location, to have a 



244 c ® ENTANGLEMENT 

particle in the same state as her particle. That is, Alice wants 
Bob to have a particle whose state will also be Q. If Alice 
measures her particle, this would not be sufficient since Q 
cannot be fully determined by measurement. One reason is 
the uncertainty principle, and another is that quantum par- 
ticles are in a superposition of several states at the same time. 
Once a measurement is taken, the particle is forced into one 
of the states in the superposition. This is called the projection 
postulate: the particle is projected onto one of the states in 
the superposition. The projection postulate of quantum 
mechanics makes it impossible for Alice to measure the state, 
Q, of her particle in such a way that she would obtain all the 
information in Q, which is what Bob would need from her in 
order to reconstruct the state of her particle on his own par- 
ticle. As usual in quantum mechanics, observing a particle 
destroys some of its information content. 

This difficulty, however, can be overcome by a clever 
manipulation, as Bennett and his colleagues understood. 
They realized that precisely the projection postulate enables 
Alice to teleport her particle's state, Q, to Bob. The act of 
teleportation sends Bob the state of Alice's particle, Q, while 
destroying the quantum state for the particle she possesses. 
This process is achieved by using a pair of entangled parti- 
cles, one possessed by Alice (and it is not her original parti- 
cle with state Q), and the other by Bob. 

Bennett and his colleagues showed that the full informa- 
tion needed so that the state of an object could be recon- 
structed is divided into two parts: a quantum part and a 
classical part. The quantum information can be transmitted 
instantaneously — using entanglement. But that information 



TELEPORTATION: "BEAM ME UP, SCOTTY" &> 24J 

cannot be used without the classical part of the information, 
which must be sent through a classical channel, limited by the 
speed of light. 

There are, therefore, two channels for the teleportation 
act: a quantum channel and a classical channel. The quantum 
channel consists of a pair of entangled particles: one held by 
Alice and the other held by Bob. The entanglement is an 
invisible connection between Alice and Bob. The connection 
is delicate, and must be preserved by keeping the particles 
isolated from their environment. A third party, Charlie, gives 
Alice another particle. The state of this new particle is the 
message to be sent from Alice to Bob. Alice can't read the 
information and send it to Bob, because — by the rules of 
quantum mechanics — the act of reading (measurement) alters 
the information unpredictably, and not all the information 
can be obtained. Alice measures a joint property of the par- 
ticle Charlie has given her and her particle entangled with 
Bob's. Because of this entanglement, Bob's particle responds 
immediately, giving him this information — the rest of it Alice 
communicates to Bob by measuring the particle and sending 
him that partial information through a classical channel. This 
information tells Bob what he needs to do with his entan- 
gled particle in order to obtain a perfect transformation of 
Charlie's particle into his own, completing the teleportation 
of Charlie's particle. It is noteworthy that neither Alice nor 
Bob ever know the state that one has sent and the other 
received, only that the state has been transmitted. The 
process is demonstrated in the figure below. 



246 C® ENTANGLEMENT 



Teleported 
State 



ALICE 




EPR-source 

Can teleportation be extended to larger objects, such as 
people? Physicists are generally reluctant to answer such a 
question, viewing it as beyond the scope of physics today, 
and perhaps in the realm of science fiction. But many scien- 
tific and technological developments have been considered 
fantasy until they became a reality. Entanglement itself was 
thought to be within the realm of the imagination until sci- 
ence proved that it is a real phenomenon, despite its bizarre 
nature. 

If teleportation of people or other large objects should be 
possible, can we envision how this might be done? This ques- 
tion, and the previous one, touch upon one of the greatest 
unsolved problems in physics: Where does the boundary lie 
separating the macro-world we know from everyday life and 
the micro-world of photons, electrons, protons, atoms, and 
molecules? 

We know from de Broglie's work that particles have a 
wave-aspect to them, and that the wavelength associated 
with a particle can be computed. Thus, in principle, even a 
person can have an associated wave-function. (There is 
another technical point here, which is beyond what we can 



TELEPORTATION: "BEAM ME UP, SCOTTY" &> Z^J 

discuss in this book, and it is that a person or another macro- 
scopic object would not be in a pure state, but rather in a 
"mixture" of states). The answer to the question as to how 
the teleportation of a person might be carried out can be 
restated as the question: Is a person the sum of many ele- 
mentary particles, each with its own wave-function, or a 
single macro-object with a single wave-function (of a very 
short wavelength)? At this point in time, no one has a clear 
answer to this question, and teleportation is therefore still a 
real phenomenon only within the realm of the very small. 



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Chapter 20 



Quantum Magic: 
What Does It All Mean? 



"The conclusions from Bell's theorem are philosophically 
startling; either one must totally abandon the realistic phi- 
losophy of most working scientists or dramatically revise 
our concept of space-time." 

— Abner Shimony and John Clauser 

"So farewell, elements of reality!" 

— David Mermin 



"W"W7"T"hat does entanglement mean? What does it tell 
* JL / us about the world and about the nature of 
V V space and time? These are probably the hardest 
questions to answer in all of physics. 

Entanglement breaks down all our conceptions about the 
world developed through our usual sensory experience. 
These notions of reality are so entrenched in our psyche that 
even the greatest physicist of the twentieth century, Albert 
Einstein, was fooled by these everyday notions into believing 
that quantum mechanics was "incomplete" because it did 
not include elements he was sure had to be real. Einstein felt 
that what happens in one place could not possibly be directly 
and instantaneously linked with what happens at a distant 
location. To understand, or even simply accept, the validity 
of entanglement and other associated quantum phenomena, 



249 



IJO Cs ENTANGLEMENT 

we must first admit that our conceptions of reality in the uni- 
verse are inadequate. 

Entanglement teaches us that our everyday experience does 
not equip us with the ability to understand what goes on at 
the micro-scale, which we do not experience directly. Green- 
stein and Zajonc (The Quantum Challenge) give an example 
demonstrating this idea. A baseball hit against a wall with 
two windows cannot get out of the room by going through 
both windows at once. This is something every child knows 
instinctively. And yet an electron, a neutron, or even an atom, 
when faced with a barrier with two slits in it, will go through 
both of them at once. Notions of causality and of the impos- 
sibility of being at several locations at the same time are shat- 
tered by the quantum theory. The idea of superposition — of 
"being at two places at once" — is related to the phenomenon 
of entanglement. But entanglement is even more dramatic, for 
it breaks down our notion that there is a meaning to spatial 
separation. Entanglement can be described as a superposition 
principle involving two or more particles. Entanglement is a 
superposition of the states of two or more particles, taken as 
one system. Spatial separation as we know it seems to evap- 
orate with respect to such a system. Two particles that can be 
miles, or light years, apart may behave in a concerted way: 
what happens to one of them happens to the other one instan- 
taneously, regardless of the distance between them. 

WHY CAN'T WE USE ENTANGLEMENT TO SEND 
A MESSAGE FASTER THAN LIGHT? 

Entanglement may violate the spirit of relativity, but not in a 
way that allows us to use it to send a message faster than 



QUANTUM MAGIC: WHAT DOES IT ALL MEAN? Co 2JI 

light. This is a very important distinction, and it captures in 
its core the very nature of quantum phenomena. The quan- 
tum world is random in its nature. When we measure, we 
force some quantum system to "choose" an actual value, 
thus leaping out of the quantum fuzz into a specific point. 
Thus, when Alice measures the spin of her particle along a 
direction she chooses (or, equivalently, measures the polar- 
ization of a photon along a direction she chooses), she can- 
not choose the result. The result will be "up" or "down," 
but Alice cannot predict what it will be. Once Alice makes 
the measurement, Bob's particle or photon is forced into a 
particular state (opposite spin along that direction, for a par- 
ticle; same polarization direction for a photon). But since 
Alice has no control over the result she gets, she can't "send" 
any meaningful information to Bob. All that can happen 
because of the entanglement is as follows. Alice can choose 
any one of many possible measurements to carry out, and, 
whichever one she chooses, she will get a result. But she 
doesn't know ahead of time which of two results she will get. 
Similarly, Bob can choose any one of many measurements to 
make and doesn't know the result ahead of time. But, 
because of the entanglement, if they happen to have chosen 
the same measurement, their unpredictable results will be 
opposite (assuming a spin measurement). 

Only after comparing their results (using a conventional 
method of communication, which cannot send information 
faster than light) can Alice and Bob see the coincidence of 
their results. 

On the face of it, there is nothing problematic about strong 
correlations; one simply introduces "elements of reality" to 



252 Cs ENTANGLEMENT 

explain them, as Einstein wanted to do. But Bell's proof leads 
us to the conclusion that this approach doesn't work. 

Abner Shimony has referred to entanglement as "passion 
at a distance," in an effort to avoid the trap of assuming that 
one can somehow use entanglement to send a message faster 
than light. Shimony believes that entanglement still allows 
for quantum mechanics and relativity theory to enjoy a 
"peaceful coexistence," in the sense that entanglement does 
not violate special relativity in a strict sense (no messages can 
travel faster than light). Other physicists, however, believe 
that the "spirit of relativity theory" still is violated by entan- 
glement, because "something" (whatever it may be) does 
"travel" faster than light (in fact, infinitely fast) between two 
entangled particles. The late John Bell was of this belief. 

Possibly a way to understand entanglement is to avoid 
looking at relativity theory altogether, and not to think of 
two entangled entities as particles "sending a message" from 
one to the other. In a paper entitled "Quantum Entangle- 
ment," Yanhua Shih argues that because two entangled par- 
ticles are (in some sense) not separate entities, there is even 
no apparent violation of the uncertainty principle, as EPR 
had suggested. 

Entangled particles transcend space. The two or three 
entangled entities are really parts of one system, and that sys- 
tem is unaffected by physical distance between its compo- 
nents. The system acts as a single entity. 

What is fascinating about the quest for entanglement is 
that a property of a quantum system was first detected by 
mathematical considerations. It is amazing that such a 
bizarre, other-worldly property would be found mathemati- 



QUANTUM MAGIC: WHAT DOES IT ALL MEAN? C© 253 

cally, and it strengthens our belief in the transcendent power 
of mathematics. After the mathematical discovery of entan- 
glement, clever physicists used ingenious methods and 
arrangements to verify that this stunning phenomenon does 
actually occur. But to truly understand what entanglement is 
and how it works is for now beyond the reach of science. 
For to understand entanglement, we creatures of reality 
depend on "elements of reality," as Einstein demanded, but 
as Bell and the experiments have taught us, these elements of 
reality simply do not exist. The alternative to these elements 
of reality is quantum mechanics. But the quantum theory 
does not tell us why things happen the way they do: why are 
the particles entangled? So a true comprehension of entan- 
glement will only come to us when we can answer John 
Archibald Wheeler's question: "Why the quantum?" 



This Page Intentionally Left Blank 



Acknowledgments 



I am most grateful to Abner Shimony, Professor Emeritus 
of Physics and Philosophy at Boston University, for his 
many hours of help, encouragement, and support to me while 
I was preparing this work. Abner has unselfishly allowed me 
to borrow many papers, books, conference proceedings, as 
well as letters and manuscripts from his personal collection 
relevant to quantum theory and entanglement. Abner spared 
no effort in answering my myriad questions on entanglement 
and the magic of quantum mechanics, explaining to me many 
obscure mathematical and physical facts about the mysteri- 
ous quantum world, and telling me the story of his own role 
in the quest for entanglement, as well as many anecdotes 
about the search for an understanding of this amazing phe- 
nomenon. Abner and I talked for many hours at his home, in 
the car, over coffee at a restaurant, while taking a walk 



155 



2j6 C® ENTANGLEMENT 

together, or late at night on the telephone and I greatly appre- 
ciate his labor of love in helping me get this story straight, as 
well as going over the manuscript and offering many sug- 
gestions for improvement and clarification. 

I wish to express my deep appreciation to Michael Home, 
Professor of Physics at Stonehill College in Massachusetts, 
for sharing with me the details of his work with Abner Shi- 
mony on designing an experiment to test Bell's inequality, 
his important work on one- two- and three-particle interfer- 
ometry, and his groundbreaking work on three-particle 
entanglement with Daniel Greenberger and Anton Zeilinger, 
widely known as the GHZ design. I am extremely grateful to 
Mike for his many hours of help to me while I was prepar- 
ing this manuscript, for answering my many questions, and 
for providing me access to many important papers and 
results. Mike carefully went over the manuscript, corrected 
many of my errors and inaccuracies, and offered many sug- 
gestions for improvement. I also thank him for kindly allow- 
ing me to adapt material on three-particle entanglement from 
his Distinguished Scholar Lecture at Stonehill College for use 
in this book. Thank you, Mike! 

I am very grateful to Alain Aspect of the Center for Optics 
Research at the University of Paris in Orsay for explaining his 
important work to me, and for teaching me some fine points 
of the theory of entangled states. Alain most kindly opened 
up his laboratory to me, showing me how he designed his 
historic experiments, built his own complex devices, and how 
he obtained his stunning results on entangled photons. I 
thank Professor Aspect for his time and effort and excite- 
ment about physics. Merci, AA. 



ACKNOWLEDGMENTS Ca> 257 

John Clauser and his colleague Stuart Freedman actually 
carried out the first experiment designed to test Bell's theory 
at Berkeley in 1972, based on the joint work with Mike 
Home, Abner Shimony, and Richard Holt (the famous 
CHSH paper). I thank John Clauser for sharing with me the 
results of his experiments and for providing me with many 
important papers on the topic of entanglement and for sev- 
eral thought-provoking interviews. 

In the years following the Clauser and Aspect experiments, 
a number of physicists around the world derived further 
results demonstrating the existence of entangled particles and 
light waves. Nicholas Gisin of the University of Geneva pro- 
duced entangled photons at great distance. Gisin has demon- 
strated entangled states for photons that were 10 kilometers 
apart, as well as studied numerous properties of entangled 
states and their use in quantum cryptography and other 
applied areas. He is also known for important theoretical 
work on Bell's theorem. Nicholas Gisin generously shared 
with me the results of his experiments, and I thank him 
warmly for providing me with many research papers pro- 
duced by his group at the University of Geneva, as well as for 
informative interviews. 

The implications of entanglement are far-reaching, and sci- 
entists are currently exploring its implications in quantum 
computing and teleportation. Anton Zeilinger of the Uni- 
versity of Vienna is a leading scientist in this area. He and his 
colleagues have demonstrated that teleportation is possible, 
at least for photons. Anton Zeilinger's work spans several 
decades and includes the pioneering work on three-particle 
entanglement, work done jointly with Greenberger and 



2j8 C© ENTANGLEMENT 

Home (GHZ), as well as entanglement swapping and other 
projects demonstrating the strange world of tiny particles. I 
am very grateful to Anton for providing me with much infor- 
mation on his work and achievements. Also in Vienna, I am 
grateful to Ms. Andrea Aglibut of Zeilinger's research group 
for providing me with many papers and documents relevant 
to the work of the group. 

I am grateful to Professor John Archibald Wheeler of 
Princeton University for welcoming me at his house in Maine 
and for discussing with me many important aspects of quan- 
tum theory. Professor Wheeler generously shared his 
thoughts about quantum mechanics and its role in our under- 
standing of the workings of the universe. His vision of quan- 
tum mechanics in the wider context of physics and 
cosmology shed much important light on the questions raised 
by Einstein, Bohr, and others about the meaning of physics 
and its place in human investigations of nature. 

I am grateful to Professor Yanhua Shih of the University of 
Maryland for an interesting interview about his many 
research projects relevant to entanglement, teleportation, and 
the method of parametric down conversion. Professor Shih 
and his colleagues were instrumental in producing some of 
the most stunning evidence for the effects of entanglement. I 
thank Yanhua for sharing with me his many research papers. 

I thank Professor Daniel Greenberger of the City Univer- 
sity of New York for information on the amazing GHZ 
experimental design and the theoretical demonstration he 
has provided jointly with Home and Zeilinger of Bell's the- 
orem in a simple and dramatic way. I am grateful to Danny 
for much information about his work. 



ACKNOWLEDGMENTS Ca> 2J9 

I am grateful to Professor William Wootters of Williams 
College in Massachusetts for an interesting interview about 
his work and on his joint "no-cloning theorem." The Woot- 
ters-Zurek theorem, which proves that there can be no quan- 
tum-mechanical "copy machine" that preserves the originals, 
has important implications in quantum theory, including 
teleportation. 

I thank Professor Emil Wolf of the University of Rochester 
for a discussion of the mysteries of light, and for important 
details about his work and the work of his late colleague 
Leonard Mandel, whose pioneering achievements exposed 
many puzzling properties of entangled photons. 

I am very grateful to Professor P.K. Aravind of the Worces- 
ter Polytechnic Institute in Massachusetts for sharing with 
me his work on entanglement. Professor Aravind has demon- 
strated surprising consequences of Bell's theorem and entan- 
gled states in a number of theoretical papers. Thank you, 
P. K., for sharing your work with me and for explaining to 
me some aspects of quantum theory. 

I thank Professor Herbert Bernstein of Hampshire College in 
Massachusetts for an interesting interview about the meaning 
of entanglement. I am also grateful to Herb for pointing out to 
me the German origin and meaning of the original term used 
by Erwin Schrodinger to describe the phenomenon. 

I am grateful to Dr. William D. Phillips of the National 
Institute of Standards and Technology, a Nobel Prize winner 
in physics, for an interesting discussion of the mysteries of 
quantum mechanics and the phenomenon of entanglement, 
as well as for providing me with interesting details of his 
work in quantum mechanics. 



26o & ENTANGLEMENT 

Dr. Claude Cohen-Tannoudji met with me in Paris and was 
both most generous with his time and informative. Cohen- 
Tannoudji is co-author of one of the classic textbooks in the 
field, Quantum Mechanics, a work that he and his colleagues 
spent five years finetuning. I thank him for his kindness, in 
readily sharing his expertise with me. 

I thank the physicist Dr. Mary Bell, John Bell's widow, for 
cooperation in my preparation of the material relating to the 
life and work of her late husband. 

I am grateful to Ms. Felicity Pors of the Niels Bohr Insti- 
tute in Copenhagen for help in facilitating the use of histor- 
ical photographs of Niels Bohr and other physicists. 

None of the experts acknowledged above are to be blamed 
for any errors or obscurities that may have remained in this 
book. 

I thank my publisher and friend, John Oakes, for his 
encouragement and support during the time I was writing 
this book. I thank the dedicated staff at Four Walls Eight 
Windows: Kathryn Belden, Jofie Ferrari-Adler, and John Bae, 
for their help and dedication in producing this book. I thank 
my wife, Debra, for her help and encouragement. 



Notes 



1. Note, however, that causation is a subtle and complicated concept 
in quantum mechanics. 

2. The New York Times, May 2, 2000, p. Fi. 

3. Richard Feynman. The Feynman Lectures.Vol. III. Reading, MA: 
Addison-Wesley, 1963. 

4. As reported by Abraham Pais. Niels Bohr's Times. Oxford: Claren- 
don Press, 1991. 

5. Much of the biographical material in this chapter is gleaned from 
Walter Moore. Schrodinger: Life and Thought. New York: Cambridge 
University Press, 1989. 

6. Walter Moore. Schrodinger: Life and Thought. New York: Cam- 
bridge University Press, 1989. 

7. M. Home, A. Shimony, and A. Zeilinger, "Down-conversion Pho- 
ton Pairs: A New Chapter In the History of Quantum Mechanical Entan- 
glement," Quantum Coherence, J.S. Anandan, ed., Singapore: World 
Scientific, 1989. 



261 



Z6z & ENTANGLEMENT 

8. E. Schrodinger, Collected Papers on Wave Mechanics, New York: 
Chelsea, 1978, 130. 

9. E. Schrodinger, Proceedings of the Cambridge Philosophical Soci- 
ety, 31 (1935) 555. 

10. Armin Hermann. Werner Heisenberg 1901-1976. Bonn: Inter 
Nations, 1976. 

11. Author's interview with John Archibald Wheeler, June 24, 2001. 

12. Wheeler, J. A., "Law without Law," contained in the collection of 
papers, Quantum Theory and Measurement, edited by J.A. Wheeler and 
W H. Zurek. Princeton, NJ: Princeton University Press, 1983. 

13. John Archibald Wheeler, "Law Without Law," Wheeler and 
Zurek, eds., p. 182-3. 

14. John Archibald Wheeler, "Law Without Law," Wheeler and 
Zurek, eds., p. 189. 

15. Much of the biographical information in this chapter is adapted 
from Macrae, Norman. John Von Neumann: The Scientific Genius Who 
Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and 
Much More. Providence, R.I.: American Mathematical Society, 1992. 

16. See Amir D. Aczel. God's Equation. New York: Four Walls Eight 
Windows, 1999. 

17. A. Folsing, Albert Einstein, New York: Viking, 1997, 

P- 477- 

18. Louis de Broglie. New Perspectives in Physics. New York: Basic 
Books, 1962, p. 150. 

19. Reported in J. A. Wheeler and W H. Zurek, eds. Quantum Theory 
and Measurement. Princeton, NJ: Princeton University Press, 1983, p. 
viii. 

20. Quoted in Wheeler and Zurek, 1983, p. 7. 

21. Abraham Pais. Niels Bohr's Times. New York: Clarendon Press, 
1991^.427. 

22. Wheeler and Zurek, p. 137. 

23. Albert Einstein, Boris Podolsky, and Nathan Rosen, "Can Quan- 
tum-Mechanical Description of Physical Reality Be Considered Com- 



NOTES C© 263 

plete?" Physical Review, 47, 777-80 (1935). 

24. Pais, 1991, p. 430. 

25. Wheeler and Zurek, 1983. 

26. A. Einstein, B. Podolsky, and N. Rosen, "Can Quantum-Mechan- 
ical Description of Physical Reality Be Considered Complete?" Physical 
Review, 47, (1935)^. 777. 

27. From the book, Albert Einstein, Philosopher Scientist, P.A. Schilpp, 
Evanston, IL: Library of Living Philosophers, 1949, p. 85. 

28. Reprinted by permission from J. Clauser, "Early History of Bell's 
Theorem," an invited talk presented at the Plenary Historical Session, 
Eighth Rochester Conference on Coherence and Quantum Optics, 2001, 
p. 11. 

29. Alain Aspect, "Trois tests experimentaux des inegalites de Bell par 
mesure de correlation de polarization de photons," A thesis for obtain- 
ing the degree of Doctor of Physical Sciences, University of Paris, Orsay, 
February 1, 1983, p. 1 

30. The ghost image experiment was reported in Y.H. Shih, "Quantum 
Entanglement and Quantum Teleportation," Annals of Physics, 10 
(2001) 1-2, 45-61. 

31. The above discussion is adapted by permission from Michael 
Home, "Quantum Mechanics for Everyone," Third Stonehill College 
Distinguished Scholar Lecture, May 1, 2001, p. 4. 

32. "Bell's Theorem Without Inequalities," by Greenberger, Home, 
Shimony, and Zeilinger, American Journal of Physics, 58 (12), December 
1990, pp. 1131-43- 

33. Reprinted from P.K. Aravind, "Borromean Entanglement of the 
GHZ State," Potentiality, Entanglement, and Passion- At- A-Distance, 53- 
59, 1997, Kluwer Academic Publishing, UK. 



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References 



Much of the work on entanglement and related physical phe- 
nomena has been published in technical journals and con- 
ference proceedings. References to the important articles in 
these areas have been made throughout the text. The fol- 
lowing is a list of more accessible references, which are more 
appropriate for the general science reader, and it includes 
only books that a reader may obtain in a good library, or 
order through a bookstore. Readers with a deeper, more tech- 
nical interest in the subject may want to track down some of 
the articles referred to in the text, especially ones appearing 
in Nature, Physics Today, or other expository journals. 



265 



z66 & ENTANGLEMENT 

BOOKS RELATED TO ENTANGLEMENT AND 
QUANTUM MECHANICS 

Bell, J. S. Speakable and Unspeakable in Quantum Mechanics. New 
York: Cambridge University Press, 1993. This book contains most 
of John Bell's papers on quantum mechanics. 

Bohm, David. Causality and Chance in Modern Physics. Philadelphia: 
University of Pennsylvania Press, 1957. 

Bohm, David. Quantum Theory. New York: Dover, 1951. 

Cohen, R., S., Home, M., and J. Stachel, eds. Experimental Meta- 
physics: Quantum Mechanical Studies for Abner Shimony. Vols. I 
and II. Boston: Kluwer Academice Publishing, 1999. These volumes, 
a festschrift for Abner Shimony, contain many research papers on 
entanglement. 

Cornwell, J. E Group Theoey in Physics. San Diego: Academic Press, 
1997. 

Dirac, P. A. M. The Principles of Quantum Mechanics. Fourth ed. 
Oxford: Clarendon Press, 1967. 

French, A. P., and E. Taylor. An Introduction to Quantum Physics. 
New York: Norton, 1978. 

Folsing, A. Albert Einstein. New York: Penguin, 1997. 

Gamow, George. Thirty Years that Shook Physics: The Story of Quan- 
tum Theory. New York: Dover, 1966. 

Gell-Mann, Murray. The Quark and the Jaguar. New York: Freeman, 
1994. 

Greenberger, D., Reiter, L., and A. Zeilinger, eds. Epistemological and 
Experimental Perspectives on Quantum Mechanics. Boston: Kluwer 
Academic Publishing, 1999. This volume contains many research 
papers on entanglement. 

Greenstein, G and A. G Zajonc. The Quantum Challenge: Modern 
Research on the Foundations of Quantum Mechanics. Sudbury, MA: 
Jones and Bartlett, 1997. 

Heilbron, J. L. The Dilemmas of an Upright Man: Max Planck and the 
Fortunes of German Science. Cambridge, MA: Harvard University 
Press, 1996. 



REFERENCES Co z6j 

Hermann, Armin. Werner Heisenberg 1901-1976, Bonn: Inter-Nations, 
1976. 

Ludwig, Giinther. Wave Mechanics. New York: Pergamon, 1968. 

Macrae, Norman. John von Neumann: The Scientific Genius Who Pio- 
neered the Modern Computer, Game Theory, Nuclear Deterrence, 
and Much More. Providence, R.I.: American Mathematical Society, 
1992. 

Messiah, A. Quantum Mechanics. Vols. I and II. New York: Dover, 
1958. 

Moore, Walter. Schrodinger: Life and Thought. New York: Cambridge 
University Press, 1989. 

Pais, Abraham. Niels Bohr's Time: In Physics, Philosophy, and Polity. 
Oxford: Clarendon Press, 1991. 

Penrose, R. The Large, the Small and the Human Mind. New York: 
Cambridge University Press, 1997. Interesting discussion of quantum 
and relativity issues, including commentaries by Abner Shimony, 
Nancy Cartwright, and Stephen Hawking. 

Schilpp, P. A., ed. Albert Einstein, Philosopher Scientist. Evanston, IL: 
Library of Living Philosophers, 1949. 

Spielberg, N., and B. D. Anderson. Seven Ideas That Shook the Uni- 
verse. New York: Wiley, 1987. 

Styer, Daniel R The Strange World of Quantum Mechanics. NewYork: 
Cambridge University Press, 2000. 

Tomonaga, Sin-Itiro. Quantum Mechanics. Vols. I and II. Amsterdam: 
North-Holland, 1966. 

Van der Waerden, B. L., ed. Sources of Quantum Mechanics. New 
York: Dover, 1967. 

Wheeler, J. A. and W H. Zurek, eds. Quantum Theory and Measure- 
ment. Princeton, NJ: Princeton University Press, 1983. This is a 
superb collection of papers on quantum mechanics. 

Wick, D. The Infamous Boundary: Seven Decades of Heresy in Quan- 
tum Physics. New York: Copernicus, 1996. 



This Page Intentionally Left Blank 



Index 



Adler, David, 37, 38 
Aharonov, Yakir, 125-26, 

127-28, 158, 170, 184 
Aharonov-Bohm effect, 126-27, 

213 
American Physical Society, 159, 

164, 167, 221 
Ampere, Andre, 33 
ancient world, 7-9, 73 
Anderson, Carl, 87 
antimatter, 70, 87 
Aravind, P. K., 232-33, 259 
Aristotle, 8 
Aspect, Alain, 256 

Bell and, 180, 185-86 
on Bell's theorem, 180 



experiments testing Bell's 
theorem, 4, 181-90, 236 

life, 177-78 

research, 178-80, 190 

Shimony's dream about, 176 
atomic cascade method, 166-6 j, 

171, 186, 191, 193 
atoms 

behavior, 53-54 

double-slit experiments, 21, 23 

recoil, 193 

structure, 40-41, 42, 44 

Babylon, 7 
Bauer, Hansi, 60 
Bell, Annie, 137 



269 



ZJO & ENTANGLEMENT 



Bell, John (father), 137 
Bell, John Stewart 

life and family, 137-39, 148 
papers, 101, 102, 144, 155, 

157, 184 
relations with other scientists, 
169, 176, 180, 185-86, 
204, 235 
research, 139-43 
response to EPR paper, 143-48 
view of relativity and entangle- 
ment, 252 
See also Bell's theorem 
Bell, Mary Ross, 139, 260 
Bell's theorem, 180-81 
assumptions, 166, 204 
criteria for testing, 128 
development of, 145-48 
experiments testing, 3-5, 147, 
1 55, 157-68, 170-75, 
181-90, 198-202, 236-38 
importance, 148, 180 
paper, 3, 144, 178-79 
research on, 209, 235 
triple entanglement and, 
217-18, 219-28 
Bennett, Charles, 242, 243, 

244 
Bernstein, Herbert, 214, 259 
Bible, 7 

big bang, 92, 156 
black-body radiation, 34-35 
black holes, 88 



Bohm, David, 184 

Aharonov-Bohm effect, 

126-27, 213 
on Clauser's experiment, 169 
criteria for tests of EPR 

paradox, 127-28 
formulation of EPR paradox, 

123-26, 127, 144, 157, 181 
life, 123 

research, 123, 158 
Bohr, Christian, 37, 39 
Bohr, Ellen Adler, 3 7 
Bohr, Harald, 38, 39 
Bohr, Margrethe, 42, 74 
Bohr, Niels 

complementarity principle, 39, 

199 
debates with Einstein, 47, 74, 
110, 111-16, 122, 159, 
180 
debate with Heisenberg on 

quantum, 88 
electron theory of metals, 39 
hydrogen atom theory, 41-44 
life and family, 37-39 
on quantum theory, 91 
relationship with Einstein, 

110-11 
relationship with Heisenberg, 

74, 77, 78 
research, 39-44, 45-46, 60, 88 
response to EPR paper, 

118-19, 121-22 



INDEX & ZJ1 



at Solvay Conferences, 61, 
110, 111-16 

students, 74, 85, 88 
Boltzmann, Ludwig, 33,56 
Borel, Emile, 50 
Born, Max, 65, 74 
Borromean rings, 232 
Borromeo family, 232 
Bose, Saryendra Nath, 53 
Bose-Einstein condensation, 54 
bosons, 208 
Boston University, 151, 152-53, 

154, 176 
Boumeester, D., 242-43 
British Atomic Energy Agency, 

139 
Broglie, Louis Victor de. See de 

Broglie, Louis Victor 
bucky balls, 24 
Burnham, D. C, 192-93 

Carnap, Rudolph, 150 

Carnot, Nicholas, 14 

Casimir, H., 88 

causality, 12, 45 

CERN. See European Center for 

Nuclear Research 
Chew, Jeffrey, 211 
Chiao, Raymond, 198 
Christiansen, Christian, 38, 39 
CHSH. See Clauser-Horne- 

Shimony-Holt (CHSH) paper 
classical mechanics, 12-13, 3 2 > 

79 



Clauser, Francis, 155-56 
Clauser, John E, 257 

belief in hidden variables 

theory, 169, 170 
CHSH paper, 166-68, 170, 

203-4 
collaboration with Shimony 

and Home, 164-65, 

167-68, 170, 174-75, 

176, 182, 203-4, 

210 
experiments testing Bell's 

theorem, 3-4, 160, 164-67, 

168-69, 1 7°~73? 1-82., 183, 

184 
Home and, 221-22 
life, 155-56 
papers on entanglement, 

174-75 
research, 156-59, 168, 174 
Clauser-Horne-Shimony-Holt 

(CHSH) paper, 166-68, 

170, 203-4 
cloning, 242 
Cohen, I. B., 153 
Cohen, Robert, 154 
Cohen-Tannoudji, Claude N., 7, 

178, 180, 260 
Colella, R., 213 
Commins, Eugene, 161, 162, 

166, 168 
complementarity, 39, 194-95, 

199 
computing, quantum, 239 



zyz 



ENTANGLEMENT 



Copenhagen interpretation of 
quantum theory, 46, 112 
Copernicus, Nicolas, 12 
Cornell, Eric, 54 
cosine waves, 64, 67-68 
cosmic radiation, 59 
cosmology, 88, 92, 156 
cryptography, 238-39 
crystals, 191-93, 200 
Curie, Marie, $6, 110 

de Broglie, Louis Victor 
on Clauser's experiment, 

169 
life, 49-50, 52 
pilot waves, 51-52, 63 
research, 50-52, 54 
at Solvay Conferences, 111 
wave properties of electrons, 

20 
wave properties of particles, 
2.1, 5^S^ 54, 61, 205, 
246 
de Broglie, Maurice, 49-50 
Debye, Peter, 61 
decoherence, 84 
delayed-choice experiments, 
92-93, 127-28, 184-85, 
187-89, 198-99 
De Martini, Francesco, 242 
derivatives, 62-63 
Descartes, Rene, 10-11, 12 
differential equations, 12, 57, 
62-63 



Dirac, Paul A. M., 70, 86-87, 

111 
dispersion-free states, 142-43 
double diamond experiment, 

215-16, 218-19 
double-slit experiments 
with atoms, 21, 23 
beam splitters, 90, 91-92 
with electrons, 21, 205 
Feynman on, 19, 156 
interference patterns, 18-19, 

21-25, 53 
with large entities, 24 
with light, 18-19, 20 
with neutrons, 21, 22, 205-6, 

207-8 
with particles, 53 
superposition of states 

demonstrated in, 25-26, 

68-69 
temporal arrangements, 198 
Wheeler's variant, 89-92 
by Young, 18-20, 68-69, 88, 

205 

earth, circumference of, 8 
Egypt, ancient, 7 
Ehrenfest, Paul, 112 
Eibl, M., 242-43 
Einstein, Albert 

Bose-Einstein condensation, 54 

career, 36 

contribution to quantum 
theory, 60, 104-6 



INDEX Co 273 



debates with Bohr, 47, 74, 

110, 111-16, 122, 159, 180 
de Broglie and, 54 
energy in light beams, 42 
on Feynman's thesis, 86 
God and dice statement, xiii, 

106, 107-8 
gravitation theory, 212-13 
on inconsistency of quantum 

theory, 90-91 
life, 103 
photoelectric effect, 20, 53, 

103, 104-6, 205 
in Princeton, 84, 116-17 
principles in nature, 108-9 
on probability, 65 
relationship with Bohr, 110-11 
at Solvay Conferences, 50, 61, 

110, 111-16 
on uncertainty principle, 

112-15 
unified theory and, 122 
view of quantum theory, xiii, 

106-8, 109, 115-16, 122, 

249 
von Neumann and, 101-2 
Wheeler's cat and, 84-85 
See also EPR (Einstein- 

Podolsky-Rosen) paper; 

relativity 
Ekert, Arthur, 238 
electricity, 32-33 
electromagnetism, 32-33, 

126-27 



electrons 
anti-, 87 

discovery of, 33, 40 
double-slit experiments, 21, 

205 
energy levels, 45 
spin, 124 

superposition of states, xi, 68 
wave properties, 20, 205 
electron theory of metals, 39 
Emeleus, Karl, 138 
energy 

conservation of, 13-14, 30 
kinetic, 33 
of photons, 105 
potential, 33 
quanta of, 34, 43 
entangled photons 

double diamond experiment, 

215-16, 218-19 
Ghost Image Experiment, 

200-202 
interference patterns, 197-98 
nonlocality, 186-87 
producing, xv, 166-6 j, 171, 

186, 191, 193, 219 
as single entity, 198, 252 
superposition of states, 197 
triple, 222-23 
Wu-Shaknov experiment, 

87-88, 126, 157, 158-59, 

160, 217 
entangled systems, 26-27, 69, 

252 



274 <*» ENTANGLEMENT 



entanglement 

applications, 238-39 
created by potentialities, 80 
definition, 70 
description in EPR paper, xv- 

xvi, 117, 120-21, 147-48, 

228-29 
descriptions, xi, 26-27, 250, 

252 
discovered by Schrodinger, 

69-70 
distances tested at, 236-37 
experimental proof, xv, 126, 

186-87 
generalized state, 233 
lack of algorithm, 176 
mathematics of, 252-53 
meaning, 249-50 
positions of particles, 214-16 
relativity and, 252 
spin of entangled particles, 

124-25 
swapping, 169 
teleportation of states, 2, 241, 

243-45 

term coined by Schrodinger, 

69? 7° 
See also triple entanglement 
entropy, 30, 33-34 
EPR (Einstein-Podolsky-Rosen) 
paper 
arguments, 119-21 
Bell's response, 143-48 
Bohm's formulation of 



paradox, 123-26, 127, 144, 

157, 181 
Bohr's response, 118-19, 

121-22 
conference on fiftieth anniver- 
sary, 215 
contradiction with quantum 

mechanics, 4, 143-44, 145, 

147, 180-81 
criteria for tests of, 127-28 
description of entanglement, 

xv-xvi, 117, 120-21, 

147-48, 228-29 
experiments consistent with, 

173-74 
experiments contradicting, xiv- 

xv, 171-72, 174, 186-87 
Heisenberg's response, 118 
importance, 120 
incompleteness of quantum 

theory, xiii, 4, 120-21, 152, 

181, 249 
lack of errors in, 152 
paradox, 121, 144-45 
publication, 117-18 
reactions to, 117-19 
Schrodinger's discussion of, 69 
See also Bell's theorem 
Eratosthenes of Cyrene, 8 
Erice (Sicily), 209-10, 220-21 
ether, 10-11 
European Center for Nuclear 

Research (CERN), 139, 140, 

179 



INDEX C® 275 



Ewald, Paul, 138 
Exner, Franz, 56 

Faraci, G., 175 
Faraday, Michael, 33 
Feynman, Richard, 19, 85-86, 

156 

fiber optics, 236-38 
fission, 88 

Fourier, Joseph B. J., 68 
Fourier analysis, 67-68 
Franson, James, 198 
Freedman, Stuart, 168-69, 

170-71 
Fry, Ed S., 174, 184 
Fuller, Buckminster, 24 

galaxies, formation of, 92 

Galileo, 9, 12, 32 

Gamow, George, 52 

Gell-Mann, Murray, 84 

Genesis , 7 

Germany, Nazi, 36, 70, 80, 81, 

116 
Ghosh, R., 195, 196 
Ghost Image Experiment, 

200-202 
GHZ entanglement, 221-22 

See also triple entanglement 
GHZ Theorem, 229-31 
Gisin, Nicholas, 4, 235-39, 257 
Glashow, Sheldon, 211 
glass, 8, 9 
Gleason, Andrew, 141-42 



Godel, Kurt, 149, 150 
gravitation theory, 32, 88, 212-13 
gravity, 207-8, 212-13 
Greece, ancient, 7-8, 73 
Greenberger, Daniel, 256, 258 
GHZ Theorem, 229-3 1 
life, 211-12 
papers on entanglement, 222, 

226 
relationship with Home and 
Zeilinger, 204, 213-15, 231, 
233-34 
research, 212-13, 21 ^ 
triple entanglement, 217-18, 
219-28 
Greene, David, 71 
Greene, Sheila May, 71 
Greenstein, G., 250 

heat, propagation of, 68 

Heisenberg, August, 73 

Heisenberg, Werner 

debate with Bohr on quantum, 

88 
lectures, ix, xi, 100 
life, 73-74, 80-81 
matrix mechanics, xiii, 74-75, 

100 
relationship with Bohr, 74, yy, 

78 
research, 74-75, 77-80 
response to EPR paper, 118 
at Solvay Conferences, 111-12 
See also uncertainty principle 



zy6 



ENTANGLEMENT 



Heisenberg's Microscope, 77-78 
Hertz, Heinrich Rudolf, 33,35 
Hess, Victor, 58-59 
hidden variables 

argument in EPR paper, 4, 

120-21, 152, 181 
Bell's work on, 141-43, 

144-48, 181 
contextual theories, 142 
disproved by experiments, 172, 

174, i75> 186, 230-31 
disproved by von Neumann, 

101, 102 
Einstein on, xiii, 107-8, 109, 

122, 152 
Gleason's theorem and, 

141-42 
Home's model, 160-61 
See also Bell's theorem 
Hilbert, David, 98, 100, 141 
Hilbert space, xii, 100, 101, 141 
Himmler, Heinrich, 80 
history, changing in experiments, 

88-92 
Hitler, Adolf, 36, 70, 80, 116 
Hoffding, Harald, 38-39, 88 
Holt, Richard 

CHSH paper, 166-68, 170, 

203-4 
experiments testing Bell's 
theorem, 163, 165, 168-69, 
170, i73-74 ? 183 
Hooke, Robert, 11 
Hopf rings, 232-33 



Home, Michael A., 256 
CHSH paper, 166-68, 170, 

203-4 
collaboration with Clauser 

and Shimony, 164-65, 

167-68, 170, 176, 182, 

203-4, 210 
collaboration with Shimony, 3, 

!5 2 -53 ? !54-55> 159-68, 

208-9 
experiments testing Bell's 

theorem, 3, 155, 159-68, 

170, 183, 184 
GHZ Theorem, 229-31 
life, 153-54 
papers on entanglement, 210, 

214-16, 219, 222, 226 
relationship with Greenberger 

and Zeilinger, 204, 213-15, 

231, 233-34 
research, 152-53, 154, 204-5, 

206-7 
on Schrodinger's discovery of 

entanglement, 69-70 
on superposition of states, 85 
triple entanglement, 217-18, 

219-28 
House Committee on Un- 
American Activities, 125 
Huygens, Christaan, 1 1 
hydrogen atom theory, 41-44 

Institute for Advanced Study, 
101, 116-17 



index c® zyy 



interference patterns 

in double-slit experiments, 

18-19, 21-25, 53 
of entangled photons, 197-98 
of neutrons, 205-6, 207-8 
as superposition of states, 
68-69 

Jauch, Josef, 142 
Joule, James, 14 
Jupiter, 9, 10 

Kasday, Len, 158, 175 

Kelvin, William, Lord, 14 

Kepler, Johann, 12 

Ketterle, Wolfgang, 54 

Kimble, H. Jeff, 194 

Kocher, Carl, 161, 162, 166, 168 

Krauss, Felicie, 58 

Lamehi-Rachti, M., 175 

Langevin, Paul, 50, 54 

lasers, 53, 173, 174, 19^-93, 
194-95 

Lavoisier, Antoine, 13 

Leibniz, Gottfried, 14 

light 

debate on nature of, 11-12 
energy in beams, 42 
as particles, 11-12, 20, 104 
propagation of, 10-11 
receptors in eyes, 18 
speed of, 8-10, 250-52 
study of, 7, 8 



wave-particle duality, x, 

20-21, i94"95> 1 99, 2.05 
wave theory, 11-12, 18, 33 
See also photons 
locality principle, 121 

contradiction with quantum 

theory, 143-44, i45> M7> 

175-76, 180-81 
disproved by experiments, 

186-87, 1 9° 
Einstein on, 108, 109, 152 
Low, Francis, 211 

Mach, Ernst, 56, 154 
Macrae, Norman, 100 
Mandel, Leonard, 194-98, 

218-19, 235 
Manhattan Project, 81, 102, 

123 
Massachusetts Institute of 

Technology. See M.I.T. 
mathematics 

lack of algorithm for entangle- 
ment, 176 
matrices, xiii, 74-75, 100 
of quantum theory, xi-xii, xiii- 
xiv, 100-101, 102, 140-41, 

i43> 147 

use in discovery of entangle- 
ment, 252-53 

von Neumann's abilities, ^y, 
98-99 

See also differential equations; 
Hilbert space 



2j8 C© ENTANGLEMENT 



matrix mechanics, xiii, 74-75, 
100 

matter 

anti-, 70, 87 
behavior, 53-54 
Bose-Einstein form, 53-54 
interaction with light, 104 
nature of, 7 

Mattle, K., 242-43 

Maxwell, James, 33, 35, 40 

Maxwell-Hertz oscillator, 3 5 

Mayer, Julius Robert, 13-14 

McCarthyism, 125 

Mermin, David, 220, 221, 223 

metals 

electron theory of, 39 
photoelectric effect, 104 

Millikan, Robert, 104 

M.I.T. (Massachusetts Institute of 
Technology), 151, 204, 
206-7, 2.1O5 2.11, 213-14 

Mittig,W., 175 

Moellenstedt, 205 

momentum 

conservation of, 13, 14-15 
of particles, 51-52, 75-76 
uncertainty principle, jj 

Moore, Walter, 61 

motion, Newton's laws of, 12 

Myrvold, Wayne, 176 

Nazi Germany, 36, 70, 80, 81, 

116 
Nernst, Walther, 110 



Neumann, John. See von 

Neumann, John 
neutron diffraction, 207 
neutrons 

double-slit experiments, 21, 
22, 205-6, 207-8 

effects of gravity, 212-13 

rotation of, 208 

thermal, 206 
Newton, Isaac, 11-13, 2 °? 3 2 ? 

153 
No Cloning Theorem, 242 
noncommutativity of matrix 
operations, 75-76, 141 
nuclear bombs, 81, 102, 123 
nuclear reactors, thermal 

neutrons, 206 
nuclear research 
in Britain, 139 
fission, 88 

in Nazi Germany, 81 
See also European Center for 
Nuclear Research 

Oppenheimer, Robert, 123 
optics, 10, 18, 51, 183, 235 
Overhauser, A. W, 213 

Pais, Abraham, 113, 118 

Pan, J.-W, 242-43 

parametric down-conversion 

technique. See spontaneous 
parametric down-conversion 
(SPDC) 



INDEX C® 275) 



particles 
anti-, 87 
cloning, 242 

momentum, 51-52, 75-76 
positions, 75, 76, 77 
probabilities, 65 
Schrodinger equation, xiv, 

62-64, 65, 67^ 68 
superposition of states, 68-69, 

85 

wave functions, 63, 64 
See also entanglement; wave- 
particle duality 
Pauli, Wolfgang, 78, 111, 

117-18 
Phillips, William D., 259 
Phoenicia, 7, 8 
photoelectric effect, 20, 33, 53, 

103, 104-6, 205 
photons, 20, 53 

double-slit experiments, 21, 

89-92 
Einstein's view of, 104-5 
energy of, 105 
polarization, 161 
superposition of states, xi 
See also entangled photons 
Physical Sciences Study Commit- 
tee, 153 
physics 

classical, 44, 62-63, 65, 153 
in nineteenth century, 32-34 
statistical, 154 
pilot waves, 51-52, 63 



Pipkin, Frank, 163, 169, 173-74, 

210 
Planck, Max 

black-body radiation, 34-35 
Bohr and, 39 
development of quantum 
theory, 29, 34, 35-36 
life and family, 29-30, 36, 70 
at Solvay Conferences, 110, 

111 
thermodynamics research, 
30-32, 34 
Planck, WilhelmJ. J., 29, 31 
Planck's constant 

in Bohr's atom theory, 41-44 
definition, 34 
measurement of uncertainty, 

77 
uses, 51-52 
in wave functions, 63 
Podolsky, Boris, 117 
See also EPR (Einstein- 
Podolsky-Rosen) paper 
polarization, 87-88, 161 
positronium, 87, 158, 175 
See also Wu-Shaknov experi- 
ment 
positrons, 87 
potentialities, 79-80 
Princeton University, 85, 123, 

125, 150 
prisms, 8 

probability, 64-67, 77^ 86, 106-7 
probability distributions, 66 



2X0 



ENTANGLEMENT 



projection postulate, 244 
Pythagoras, 8 

quantum, definition of, x, 34 
quantum cryptography, 238-39 
quantum electrodynamics, 87 
quantum eraser, 199 
quantum mechanics 

distinction from classical 

mechanics, 79 
randomness, 251 
sum-over-histories approach, 
86 
quantum teleportation. See 

teleportation 
quantum theory 

Copenhagen interpretation, 46, 

112 
debates on, 46-47 
definition, x 
distinction from classical 

physics, 212, 246 
experiments supporting, xiv- 
xv, 171-72, 174, 186-87, 
190 
general formulations, 45 
mathematical basis, 100-101, 

102, 140-41, 143, 147 
Planck's development of, 29, 

34,35-36 
seen as incomplete by Einstein, 

xiii, 109, 120-21, 152, 

249 
See also hidden variables 
quasars, 92-93 



radiation 

black-body, 34-35 

microwave, 156 

X-rays, 49-50 
radioactivity, 56, 58-59 
Ratz, Laslo, 98 

Rauch, Helmut, 205-6, 208, 209 
Rayleigh, John, 40 
Rayleigh-Jeans law, 3 5 
realism principle, 108, 109, 119, 

143-44, 152, 249 
Redhead, Michael, 220, 221 
relativity 

entanglement and, 238 

general, 106, 114-15 

in quantum mechanics, 13, 
212-13, 2 5 2 

special, 87, 103, 106, 238, 252 

theory of, 12-13 
Rella, Lotte, 56 
Rome, ancient, 8, 9 
Romer, Olaf, 10, 11, 12 
Rosen, Nathan, 117 

See also EPR (Einstein- 
Podolsky-Rosen) paper 
Rosenfeld, Leon, 114, 115-16, 

118 
Rutherford, Lord James, 40-41, 
4 2 , 44, 45 

Sarachik, Myriam, 211 
Schrodinger, Anny Bertel, 59, 60, 

61, 71 
Schrodinger, Erwin 



INDEX & 2X1 



affairs, 56, 58, 60, 61-62, 71 
agreement with Einstein on 

quantum theory, 74 
discovery of entanglement, 

69-70 
Einstein and, 117 
family, 71, 234 
life, 55-57, 58, 59, 60, 61-62, 

70-71 
reaction to EPR paper, 119 
research, 52, 57-58, 59-62, 

69-70, 100, 179 
at Solvay Conferences, 111 
Schrodinger equation, xiv, 62-64, 

65, 6y, 68 
Schrodinger's Cat, 83-84 
Seneca, 8 
Shaknov, Irving, 87 

See also Wu-Shaknov experi- 
ment 
Shih, Yanhua, 198-202, 219, 

252, 258 
Shimony, Abner, 102, 179, 221, 
259 
on Bell, 147 
CHSH paper, 166-68, 170, 

203-4 
collaboration with Clauser and 
Home, 164-65, 167-68, 

170, 174-75 ? 176 ? !82, 
203-4, 210 

collaboration with Home, 3, 

!5 2 -53> !54-55> 159-68, 
208-9 



description of entanglement, 

252 
dreams, 176 
experiments testing Bell's 

theorem, 159-68, 170, 183 
life and family, 149-50 
papers on entanglement, 

174-75, 210, 222, 226 
research, 150-53 
on Schrodinger's discovery of 
entanglement, 69-70 
Shugart, Howard, 174 
Shull, Cliff, 204, 206-7, 2,10—11, 

213, 214 
Sicily. See Erice 
sine waves, 64, 67-68 
singlet state, 124 
Snider, Joseph, 161 
Solvay, Ernest, 109-10 
Solvay Conferences, 50-51, 61, 

109, 110, 111-16 
Sommerfeld, Arnold, 74 
sound waves, 50 

SPDC. See spontaneous paramet- 
ric down-conversion 
special relativity, 87, 103, 106, 

238, 252 
spin, 124-25, 212, 232 
spontaneous parametric down- 
conversion (SPDC), 191-94, 
195-96, 198, 200, 219 
"Star Trek," 2, 241 
statistical physics, 154 
Stern, Otto, 111 



282 



ENTANGLEMENT 



Stonehill College, 206, 223 
Styer, David, 223 
sum-over-histories approach to 

quantum mechanics, 86 
superposition of states, xi, 85 

cat analogies, 83-85 

definition, 25 

demonstrated in double-slit 
experiments, 25-26, 68-69 

in entanglement, 197, 250 

in triple entanglement, 226 

of waves, 67-69 

Taddeus, Patrick, 156 
telephone companies, 236, 237, 

238-39 
teleportation 

channels, 244-45 

definition, 241, 242 

experiments, 241-42 

potential for humans, 246-47 

process, 243-45 

quantum, 2, 202, 241, 243-45 
Teller, Edward, 99-100 
thermal neutrons, 206 
thermodynamics, 30-32, 34 
Thompson, Randal C, 174, 184 
Thomson, J. J., 33,40-41 
Tonomura, A., 21 
Townes, Charles, 168, 173 
triple entanglement, 2-3, 217-18, 
219-28 

Borromean rings and, 232 



experiments, 229 
GHZ Theorem, 229-31 
Hopf rings and, 232-33 
mathematical statement, 

226-27 
producing, 222 
proof, 204 

Ullman, J., 158, 175 
ultraviolet catastrophe, 34-35 
uncertainty principle, x-xi, xiii, 
76, 106-7 
Bohr's proof, 114 
Einstein on, 112-15, 1:L 8 
Heisenberg's Microscope, 

77-78 
importance, 76-77 
in teleportation, 243, 244 
universe, creation of, 92, 156 
University of California at 

Berkeley, 168-69, x 74? 211 
University of Vienna, 56-57, 58, 
234 

Venice, 9 

von Karman, Theodore, 99-100 
von Neumann, John 
life and family, 95-100 
mathematics of quantum 
theory, 100-101, 102, 
140-41, 143, 147 
relationship with Einstein, 



INDEX © 2 S3 



von Neumann, Margaret, 95-98 
von Neumann, Max, 95-98 
von Neumann, Michael, 96 
von Neumann, Nicholas, 96 

wave functions, 107 

associated with humans, 246 

noncommutative operations, 
75-76 

of particles, 63, 64 

square of amplitude, 6$, 66, 
67, 107 

superposition, 67-68 
wave-particle duality, x, 53 

complementarity, 194-95, 199 

de Broglie's discovery of, 21, 

5^5^ 54, 61, ^05 

Einstein on, 205 

Schrodinger equation, xiv, 
62-64, 65, 6j, 68 

shown with double-slit 
experiments, 21-25 
waves 

amplitudes, 86 

radio, 50 

sound, 50 
wave theory 

de Broglie's work on, 51 

of light, 11-12, 18, 33 

See also interference patterns 
Weiman, Carl, 54 
Weinberg, D. L., 192-93 
Weinberg, Steven, 211 



Weinfurter, H., 242-43 
Werner, Sam, 205-6, 207-8, 

213 
Weyl, Hermann, 61 
Wheeler, John Archibald, 253, 258 

cat, 84-85 

influence on Shimony, 150 

life, 85-86, 88 

research, 87, 88-93 
Wheeler's Cat, 84-85 
Wightman, Arthur, 152 
Wigner, Eugene, 99, 102, 150, 

164 
Willis, Charles, 3, 154 
Wolf, Emil, 235, 259 
Wootters, William, 242, 259 
World War I, 59 
World War II, 70-71,81 
Wu, Chien-Shiung, 87, 158-59, 

175 

See also Wu-Shaknov experi- 
ment 
Wu-Shaknov experiment, 87-88, 
1 57, 158-59, i^o, 217 

Bohm-Aharonov paper on, 
126, 158 

X-rays, 49-50 

Young, Thomas 

double-slit experiments, 

18-20, 68-69, 88, 205 
life and career, 17-18 



284 Ccs ENTANGLEMENT 



Zajonc, A. G., 250 
Zeilinger, Anton, 190, 257-258 
bucky ball experiments, 23-24 
collaboration with Home, 

210-11 
entanglement experiments, 236 
GHZ Theorem, 229-31 
life, 209 
neutron interference patterns, 

22 
papers on entanglement, 

214-16, 219, 222, 226 



relationship with Greenberger 

and Home, 204, 213-15, 

231, 233-34 
research, 209-11, 213, 218, 

234 
on Schrodinger's discovery of 

entanglement, 69-70 
teleportation experiments, 

242-43 
triple entanglement, 219-28, 

229 
Zurek, W., 242